DOCSLIB.ORG

Notices of the American Mathematical Society

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Notices of the American Mathematical Society OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings . 706 Program for the Meeting in Laramie, Wyoming . 707 Abstracts for the M·~eting - Pages 758-800 PRELIMINARY ANNOUNCEMENTS OF MEETINGS . • . • • . • . • . 731 LETTERS TO THE .EDITOR . • . • . • . • . 733 PERSONAL ITEMS .........•...••......•................•... 735 NEW AMS PUBLICATIONS . • . • . • . • . • . 737 ACTIVITIES OF OTHER ASSOCIATIONS. • . • . 739 MEMORANDA TO MEMBERS Mathematical Sciences Employment Register . 741 NEWS ITEMS AND ANNO'JNCEMENTS. • . • . 742 VISITING MATHEMATICIANS. • . • . • . • . 747 BACKLOG FOR MATHEMATICAL RESEARCH JOURNALS . • . • • . • . • . 756 ABSTRACTS OF CONTRIBUTED PAPERS. • . • . • . 757 ERRATA •..•.•...•.•.•....•..•......•..•....••.•..•....... 850 INDEX TO ADVERTISERS . • • • . • . 856 MEETINGS Calendar of Meetings NOTE: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the cJVoticei) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet- Deadline ing Date Place for No. Abstracta• 678 October 31, 1970 Washington, D. C. Sept, 10, 1970 679 November 20-21, 1970 Athens, Georgia Oct, '6, 1970 680 November 21, 1970 Pasadena, California Oct, 6, 1970 681 November 28, 1970 Urbana, Illinois Oct, 6, 1970 682 January 21-25, 1971 Atlantic City, New Jersey Nov. 5, 1970 (77th Annual Meeting) March 26-27, 1971 Chicago, Illinois April 7-10, 1971 New York, New York April 24, 1971 Monterey, California August 30-Sep:ember 3, 1971 University Park, Pennsylvania (76th Summer Meeting) January 17-21, 1972 Las Vegas, Nevada (78th Annual Meeting) *The abstracts of papers to be presented in person at the meetings must be received in the Head­ quarters Offices of the Society in Providence, Rhode Island, on or before these deadlines, The dead­ lines also apply to news items. The next two deadlines for by-title abstracts will be September 3, 1970, and September 2 9, 1970, . OTHER EVENTS September 1-10, 1970 International Congress of Mathematicians Nice, France --~-···---· The cJI/Oiiai) of the American Mathematical Society is published by the American Mathematical Society, 321 South Main Street, P. 0. Box 6248, Providence, Rhode Island 02904 in January, February, April, June, August, October, November and December. Price per annual volume is $10.00. Price per copy $3.00. Special price for copies sold at registration desks of meetings of the Society • $1.00 per copy. Subscriptions, orders for back numbers (back issues of the last two years only are available) and inquiries sho~d be addressed to the American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02904. Second class postage p81d at Providence, Rhode Island, and additional mailing offices. Copyright © 1970 by the American Mathematical Society Printed in the United States of America 706 The Seventy-Fifth Summer Meeting University ofWyoming Laramie, Wyoming August25-28,1970 The seventy-fifth summer meeting The first award of the Norbert of the American Mathematical Society will Wiener Prize in Applied Mathematics be held at the University of Wyoming, will be made at 2:15 p.m. on Tuesday, Laramie, Wyoming, from Tuesday, August August 25, in the Auditorium of the Arts 25, through Friday, August 28, 1970. All and Sciences Building. There will be sessions of the meeting will be held on the numerous sessions for contributed ten­ campus of the University. The times listed minute papers. These are scheduled at below for events of the meeting are 3:15 p.m. on Tuesday, 10:15 a.m. on MOUNTAIN DAYLIGHT SAVING TIME Wednesday, at 10:15 a.m. and 2:15 p.m. throughout. on Thursday, and at 10:15 a.m. on Friday. The Colloquium Lectures will be Late papers will not be accepted for given by Professor R. H. Bing of the Uni­ presentation at this meeting. versity of Wisconsin. The title of this This meeting will be held in con­ series of lectures is "Topology of 3-mani­ junction with meetings of the Mathematical folds." The Colloquium Lectures will be Association of America, the Institute of presented at 1:00 p.m. on Tuesday, August Mathematical Statistics, and Pi Mu Epsi­ 25, in the Auditorium of the Arts and lon. The Mathematical Association of Sciences Building1 and at 9:00 a.m. on America will meet from Monday through Wednesday, Thursday, and Friday, August Wednesday. The Association will present 26-28, in Room 302 of the Classroom Professor Harry Kesten of Cornell Uni­ Building. versity as the Earle Raymond Hedrick By invitation of the Committee to Lecturer. The title of Professor Kesten's Select Hour Speakers for Annual and series of lectures will be "Escapades of a Summer Meetings, there will be two random walk." The Institute of Mathemati­ invited hour addresses at the meeting. cal Statistics will meet from Monday Professor Patrick P. Billingsley of the through Friday. The Wald Lectures, spon­ University of Chicago will speak on sored by the IMS, will be given by Profes­ Thursday, August 27, at 1:00 p.m. in the sor Murray Rosenblatt of the University Auditorium of the Arts and Sciences Build­ of California, San Diego. The subject of ing. The title of his lecture is "Some these lectures is "Topics in estimation probability results connected with Dio­ for stationary processes." Pi Mu Epsilon phantine approximation." Professor Srini­ will meet concurrently with the Society and vasa S. R. Varadhan of the Courant In­ the Association. stitute oJ Mathematical Sciences, New York University, will present an address en­ titled "Diffusion processes: a martingale approach." This lecture will be given at COUNCIL AND BUSINESS MEETING 1:00 p.m. on Friday, August 28, in the Auditorium of the Arts and Sciences The Council of the Society will meet Building. 707 on Tuesday, August 25, at 5:00p.m. in the BOOK SALES Rendezvous Room of the Washakie Center. There will be no book sale at this The Business Meeting of the Society will meeting. be held on Thursday, August 27, at4:00 p.m. in the Auditorium of the Arts and Sciences DORMITORY HOUSING Building. Rooms are available in a new dormi­ A proposed amendment to the By­ tory complex surrounding Washakie Cen­ laws, approved by the Council, is to be ter, registration headquarters. Dormitor­ submitted to the membership at the Busi­ ies have elevators and lounges, with ness Meeting. The effects are to make the kitchenettes on each floor. Coin-operated Committee to Monitor Problems in Com­ washers and dryers, as well as ironing munications be a statutory committee, boards and irons, are available. with members nominated by the nominating Rooms may be occupied from 2:00 committee and elected by the membership; p.m. Saturday, August 22, until Saturday to make the chairman of the committee, noon, August 29. Bed linens, blankets, elected by the committee, be a member of towels and soap will be provided, but the Council; to make the current members maid service is not available. The rates of the appointed committee be the initial are: $4.00 per day I per person, double elected members with staggered terms; occupancy, and $6.00 per day, single. No and to charge the committee with per­ additional charge is made for cribs in the formance of such tasks in the field of rooms, but the university cannot provide communication of mathematics as are them. Cribs can be rented from Smith's assigned to it by the Council. Outlet, 414 South Second Street (307-742- 2510) at $3.00 per week. Guests are ex­ REGISTRATION pected to pay for their rooms at the time The Registration Desk will be in the they check in. lobby of the Washakie Center. It will be Upon arrival, all guests should open on Sunday from 2:00 p.m. to 8:00 check in at Washakie Center to register p.m.; on Monday from 8:00 a.m. to 5:00 for dormitory rooms. Turn north from p.m.; on Tuesday, Wednesday, and Thurs­ Grand Avenue (U. S. 30 and Business In­ day from 9:00 a.m. to 5:00 p.m. and on terstate 80) on 15th Street, and then east Friday from 9:00 a.m. to 1:00 p.m. The at the first corner on !vinson Avenue. The telephone number will be 307-766-4340. registration area is on the lower level of The registration fees will be as Washakie Center. Dormitory personnel follows: will be on duty 24 hours a day to issue Members $5.00 keys. Student bellhops, who will accept Students $ 1.00 tips, will be available if desired. Nonmembers $10.00 Guests must register in advance to be assured of dormitory housing, using the There will be no extra charge for form provided on page 704 of the june of the families of registered members c)lotiaiJ • Dormitory reservations will be participants. confirmed by the housing office of the Uni­ versity of Wyoming. It is probable that EMPLOYMENT REGISTER room will be available for those who do not The joint Committee on Employ­ register in advance, but this cannot be ment Opportunities has decided not to guaranteed. have an Employment Register at the Laramie, Wyoming, meeting. FOOD SERVICES The dining room in Washakie Cen­ EXHIBITS ter will be open for lunch on Sunday, Aug­ Book exhibits and exhibits of edu­ ust 23, and will serve meals through break­ cational media will be displayed in the fast, Saturday, August 29, except during Wyoming Room of the Washakie Center the Buffalo Roast Wednesday evening. on Tuesday, Wednesday, and Thursday.
Load more

Recommended publications
  • A Small Complete Category
    Annals of Pure and Applied Logic 40 (1988) 135-165 135 North-Holland A SMALL COMPLETE CATEGORY J.M.E. HYLAND Department of Pure Mathematics and Mathematical Statktics, 16 Mill Lane, Cambridge CB2 ISB, England Communicated by D. van Dalen Received 14 October 1987 0. Introduction This paper is concerned with a remarkable fact. The effective topos contains a small complete subcategory, essentially the familiar category of partial equiv- alence realtions. This is in contrast to the category of sets (indeed to all Grothendieck toposes) where any small complete category is equivalent to a (complete) poset. Note at once that the phrase ‘a small complete subcategory of a topos’ is misleading. It is not the subcategory but the internal (small) category which matters. Indeed for any ordinary subcategory of a topos there may be a number of internal categories with global sections equivalent to the given subcategory. The appropriate notion of subcategory is an indexed (or better fibred) one, see 0.1. Another point that needs attention is the definition of completeness (see 0.2). In my talk at the Church’s Thesis meeting, and in the first draft of this paper, I claimed too strong a form of completeness for the internal category. (The elementary oversight is described in 2.7.) Fortunately during the writing of [13] my collaborators Edmund Robinson and Giuseppe Rosolini noticed the mistake. Again one needs to pay careful attention to the ideas of indexed (or fibred) categories. The idea that small (sufficiently) complete categories in toposes might exist, and would provide the right setting in which to discuss models for strong polymorphism (quantification over types), was suggested to me by Eugenio Moggi.
    [Show full text]
  • Quantum Duality, Unbounded Operators, And
    JOURNAL OF MATHEMATICAL PHYSICS 51, 063511 ͑2010͒ Quantum duality, unbounded operators, and inductive limits ͒ Anar Dosia Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10, Turkey ͑Received 20 October 2009; accepted 7 April 2010; published online 14 June 2010͒ In this paper, we investigate the inductive limits of quantum normed ͑or operator͒ spaces. This construction allows us to treat the space of all noncommutative con- tinuous functions over a quantum domain as a quantum ͑or local operator͒ space of all matrix continuous linear operators equipped with S-quantum topology. In par- ticular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens–Mackey theorem. Further, the inductive limits of operator spaces are used to introduce locally compact and lo- cally trace class unbounded operators on a quantum domain and prove the dual realization theorem for an abstract quantum space. © 2010 American Institute of Physics. ͓doi:10.1063/1.3419771͔ I. INTRODUCTION The operator analogs of locally convex spaces have been started to develop in Ref. 14 by Effros and Webster. The central goal of this direction is to create a theory of quantum polynormed spaces or quantum spaces, which should reflect the “locally convex space chapters” of quantum functional analysis. This theory has been created as the basic language of quantum physics. To have a comprehensive mathematical model of quantum physics, it is necessary to consider the linear spaces of unbounded Hilbert space operators or “noncommutative variable spaces.”19 This is the mathematical background of Heisenberg’s “matrix mechanics.” The quantizations of a variable space have provided functional analysis with the new constructions, methods, and problems.22 Being a new and modern branch of functional analysis, quantum functional analysis can be divided into the normed13,20 and polynormed ͑or locally convex͒ topics,14,25 as in the classical theory.
    [Show full text]
  • Mathematicians Fleeing from Nazi Germany
    Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D.
    [Show full text]
  • Rudi Mathematici
    Rudi Mathematici Y2K Rudi Mathematici Gennaio 2000 52 1 S (1803) Guglielmo LIBRI Carucci dalla Somaja Olimpiadi Matematiche (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE P1 (1912) Boris GNEDENKO 2 D (1822) Rudolf Julius Emmanuel CLAUSIUS Due matematici "A" e "B" si sono inventati una (1905) Lev Genrichovich SHNIRELMAN versione particolarmente complessa del "testa o (1938) Anatoly SAMOILENKO croce": viene scritta alla lavagna una matrice 1 3 L (1917) Yuri Alexeievich MITROPOLSHY quadrata con elementi interi casuali; il gioco (1643) Isaac NEWTON consiste poi nel calcolare il determinante: 4 M (1838) Marie Ennemond Camille JORDAN 5 M Se il determinante e` pari, vince "A". (1871) Federigo ENRIQUES (1871) Gino FANO Se il determinante e` dispari, vince "B". (1807) Jozeph Mitza PETZVAL 6 G (1841) Rudolf STURM La probabilita` che un numero sia pari e` 0.5, (1871) Felix Edouard Justin Emile BOREL 7 V ma... Quali sono le probabilita` di vittoria di "A"? (1907) Raymond Edward Alan Christopher PALEY (1888) Richard COURANT P2 8 S (1924) Paul Moritz COHN (1942) Stephen William HAWKING Dimostrare che qualsiasi numero primo (con (1864) Vladimir Adreievich STELKOV l'eccezione di 2 e 5) ha un'infinita` di multipli 9 D nella forma 11....1 2 10 L (1875) Issai SCHUR (1905) Ruth MOUFANG "Die Energie der Welt ist konstant. Die Entroopie 11 M (1545) Guidobaldo DEL MONTE der Welt strebt einem Maximum zu" (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR Rudolph CLAUSIUS 12 M (1906) Kurt August HIRSCH " I know not what I appear to the world,
    [Show full text]
  • Spectral Measures in Locally Convex Algebras by Helmut H
    SPECTRAL MEASURES IN LOCALLY CONVEX ALGEBRAS BY HELMUT H. SCHAEFER The University of Michigan, U.S.A.Q) Introduction The central subject of classical spectral theory has been the spectral representation of self-adjoint and normal operators in Hilbert space; after Hilbert had given a complete treatment of the bounded case, the spectra] theory of unbounded self-adjoint and normal operators was developed by yon Neumann and others. (An excellent account can be found in [23].) Abstractions of algebras of Hermitian and normal operators were considered by various authors, notably Stone [22] who characterized such algebras as algebras of conti- nuous functions on a compact (Hausdorff) space. Investigations by Freudenthal [9] and Nakano [15] (especially papers 1 and 2), also leading to spectral theories, went in a different direction. Generalizations of unitary operators to reflexive Banach spaces were considered by Lorch [13]; Lorch also developed an operational calculus for those operators in reflexive Banach spaces that can be represented by a spectral measure [12]. (Taylor [24] developed such a calculus for closed operators on a Banach space whose spectrum does not cover the plane, but necessarily restricted to functions locally holomorphic on the spectrum. There are some recent results in this direction for operators on a locally convex space [26], [16].) The most extensive work on bounded and unbounded operators in a Banach space is due to Dunford, Schwartz, Bade and others (for a detailed bibliography, see [6] and [8]). Dunford considers operators that have a countably additive resolution of the identity, but may differ from a spectral operator (in the sense of Definition 4, Section 4 of this paper) by a quasi-nilpotent.
    [Show full text]
  • Algebraic Cocompleteness and Finitary Functors
    Logical Methods in Computer Science Volume 17, Issue 2, 2021, pp. 23:1–23:30 Submitted Feb. 27, 2020 https://lmcs.episciences.org/ Published May 28, 2021 ALGEBRAIC COCOMPLETENESS AND FINITARY FUNCTORS JIRˇ´I ADAMEK´ ∗ Department of Mathematics, Czech Technical University in Prague, Czech Republic Institute of Theoretical Computer Science, Technical University Braunschweig, Germany e-mail address: [email protected] Abstract. A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. Example: assuming GCH, the category Set≤λ of sets of power at most λ has that property, whenever λ is an uncountable regular cardinal. For all finitary (and, more generally, all precontinuous) set functors the initial algebra and terminal coalgebra are proved to carry a canonical partial order with the same ideal completion. And they also both carry a canonical ultrametric with the same Cauchy completion. Finally, all endofunctors of the category Set≤λ are finitary if λ has countable cofinality and there are no measurable cardinals µ ≤ λ. 1. Introduction The importance of terminal coalgebras for an endofunctor F was clearly demonstrated by Rutten [Rut00]: for state-based systems whose state-objects lie in a category K and whose dynamics are described by F , the terminal coalgebra νF collects behaviors of individual states. And given a system A the unique coalgebra homomorphism from A to νF assigns to every state its behavior. However, not every endofunctor has a terminal coalgebra. Analogously, an initial algebra µF need not exist. Freyd [Fre70] introduced the concept of an algebraically complete category: this means that every endofunctor has an initial algebra.
    [Show full text]
  • Nakayama Categories and Groupoid Quantization
    NAKAYAMA CATEGORIES AND GROUPOID QUANTIZATION FABIO TROVA Abstract. We provide a precise description, albeit in the situation of standard categories, of the quantization functor Sum proposed by D.S. Freed, M.J. Hopkins, J. Lurie, and C. Teleman in a way enough abstract and flexible to suggest that an extension of the construction to the general context of (1; n)-categories should indeed be possible. Our method is in fact based primarily on dualizability and adjunction data, and is well suited for the homotopical setting. The construction also sheds light on the need of certain rescaling automorphisms, and in particular on the nature and properties of the Nakayama isomorphism. Contents 1. Introduction1 1.1. Conventions4 2. Preliminaries4 2.1. Duals4 2.2. Mates and Beck-Chevalley condition5 3. A comparison map between adjoints7 3.1. Projection formulas8 3.2. Pre-Nakayama map 10 3.3. Tensoring Kan extensions and pre-Nakayama maps 13 4. Nakayama Categories 20 4.1. Weights and the Nakayama map 22 4.2. Nakayama Categories 25 5. Quantization 26 5.1. A monoidal category of local systems 26 5.2. The quantization functors 28 5.3. Siamese twins 30 6. Linear representations of groupoids 31 References 33 arXiv:1602.01019v1 [math.CT] 2 Feb 2016 1. Introduction A k-extended n-dimensional C-valued topological quantum field theory n−k (TQFT for short) is a symmetric monoidal functor Z : Bordn !C, from the (1; k)-category of n-cobordisms extended down to codimension k [CS, Lu1] to a symmetric monoidal (1; k)-category C. For k = 1 one recovers the classical TQFT's as introduced in [At], while k = n gives rise to fully Date: October 22, 2018.
    [Show full text]
  • Professor ADDRESS: Department of Mathematics University of Florida
    CURRICULUM VITAE NAME: Krishnaswami Alladi PRESENT POSITION: Professor ADDRESS: Department of Mathematics University of Florida Gainesville, Florida 32611 Ph: (352) 294-2290 e-mail: alladik@ufl.edu BORN: October 5, 1955 Trivandrum, India DEGREES: Ph.D., U.C.L.A. - 1978; Advisor-E.G. Straus M.A., U.C.L.A. - 1976 B.Sc., Madras University, India - 1975 RESEARCH INTERESTS: Number Theory - Analytic Number Theory, Sieve Methods, Probabilistic Number Theory, Diophantine Approximations, Partitions, q-hypergeometric identities PROFESSIONAL EXPERIENCE: T.H. Hildebrandt Research Assistant Professor, University of Michigan, Ann Arbor, Michigan, 1978-1981. Visiting Member, Institute for Advanced Study, Princeton, New Jersey, 1981-1982. Visiting Associate Professor, University of Texas, Austin, Texas, 1982-1983. Visiting Associate Professor, University of Hawaii, Honolulu, Hawaii, 1984-1985. Associate Professor, Institute of Mathematical Sciences, Madras, India, 1981-1986. Associate Professor, University of Florida, 1986-1989. Professor, University of Florida, 1989-present. Visiting Professor, Pennsylvania State University, University Park, Pennsylvania, in 1992-93 (on sabbatical from University of Florida) and in Fall 1994. Chairman, Department of Mathematics, University of Florida, 1998-2008 AWARDS AND HONORS: Chancellor's Fellowship for the Ph.D., 1975-78, UCLA. Alumni Medal for one of 5 best Ph.D. theses (all subjects) at UCLA in 1978. CLAS Research Awards at University of Florida thrice: 1987, 1994, 2000 TIP Award for distinguished teaching at the University of Florida in 1994-95. STEP/SPP Awards for distinguished performance in the rank of Full Professor at the University of Florida twice: 2001, 2010. Elected Fellow of the American Mathematical Society in 2012-13 during inaugural year of the Fellows Program of the AMS.
    [Show full text]
  • Subspaces and Quotients of Topological and Ordered Vector Spaces
    Zoran Kadelburg Stojan Radenovi´c SUBSPACES AND QUOTIENTS OF TOPOLOGICAL AND ORDERED VECTOR SPACES Novi Sad, 1997. CONTENTS INTRODUCTION::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 I: TOPOLOGICAL VECTOR SPACES::::::::::::::::::::::::::::::: 3 1.1. Some properties of subsets of vector spaces ::::::::::::::::::::::: 3 1.2. Topological vector spaces::::::::::::::::::::::::::::::::::::::::: 6 1.3. Locally convex spaces :::::::::::::::::::::::::::::::::::::::::::: 12 1.4. Inductive and projective topologies ::::::::::::::::::::::::::::::: 15 1.5. Topologies of uniform convergence. The Banach-Steinhaus theorem 21 1.6. Duality theory ::::::::::::::::::::::::::::::::::::::::::::::::::: 28 II: SUBSPACES AND QUOTIENTS OF TOPOLOGICAL VECTOR SPACES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 39 2.1. Subspaces of lcs’s belonging to the basic classes ::::::::::::::::::: 39 2.2. Subspaces of lcs’s from some other classes :::::::::::::::::::::::: 47 2.3. Subspaces of topological vector spaces :::::::::::::::::::::::::::: 56 2.4. Three-space-problem for topological vector spaces::::::::::::::::: 60 2.5. Three-space-problem in Fr´echet spaces:::::::::::::::::::::::::::: 65 III: ORDERED TOPOLOGICAL VECTOR SPACES :::::::::::::::: 72 3.1. Basics of the theory of Riesz spaces::::::::::::::::::::::::::::::: 72 3.2. Topological vector Riesz spaces ::::::::::::::::::::::::::::::::::: 79 3.3. The basic classes of locally convex Riesz spaces ::::::::::::::::::: 82 3.4. l-ideals of topological vector Riesz spaces :::::::::::::::::::::::::
    [Show full text]
  • Internal Groupoids and Exponentiability
    VOLUME LX-4 (2019) INTERNAL GROUPOIDS AND EXPONENTIABILITY S.B. Niefield and D.A. Pronk Resum´ e.´ Nous etudions´ les objets et les morphismes exponentiables dans la 2-categorie´ Gpd(C) des groupoides internes a` une categorie´ C avec sommes finies lorsque C est : (1) finiment complete,` (2) cartesienne´ fermee´ et (3) localement cartesienne´ fermee.´ Parmi les exemples auxquels on s’interesse´ on trouve, en particulier, (1) les espaces topologiques, (2) les espaces com- pactement engendres,´ (3) les ensembles, respectivement. Nous considerons´ aussi les morphismes pseudo-exponentiables dans les categories´ “pseudo- slice” Gpd(C)==B. Comme ces dernieres` sont les categories´ de Kleisli d’une monade T sur la categorie´ “slice” stricte sur B, nous pouvons appliquer un theor´ eme` gen´ eral´ de Niefield [17] qui dit que si T Y est exponentiable dans une 2-categorie´ K, alors Y est pseudo-exponentiable dans la categorie´ de Kleisli KT . Par consequent,´ nous verrons que Gpd(C)==B est pseudo- cartesienne´ fermee,´ lorsque C est la categorie´ des espaces compactement en- gendres´ et chaque Bi est faiblement de Hausdorff, et Gpd(C) est localement pseudo-cartesienne´ fermee´ quand C est la categorie´ des ensembles ou une categorie´ localement cartesienne´ fermee´ quelconque. Abstract. We study exponentiable objects and morphisms in the 2-category Gpd(C) of internal groupoids in a category C with finite coproducts when C is: (1) finitely complete, (2) cartesian closed, and (3) locally cartesian closed. The examples of interest include (1) topological spaces, (2) com- pactly generated spaces, and (3) sets, respectively. We also consider pseudo- exponentiable morphisms in the pseudo-slice categories Gpd(C)==B.
    [Show full text]
  • Ann I J V 2 E 5 R S R
    ANN I J V 2 E 5 R S R J A STUDENT NNEWSPAPERE W S 1 Z3 25 billion alumni backbone Art a memorial killed CPS They might be gone people can donate both money and of alumna but they certainly are not forgotten services By Laura Hosmer Alumni in feet are on the minds Weve seen a dramatic in- As friends of Susan Con well a of college administrators even more crease in the number of volunteers 1991 graduate of Ohio Wesleyan often these days playing an in- said Richard Tantillo director of deal with the shock and pain of her creasingly large role in keeping development at Rensselaer Poly- X murder many reflect upon the art affordable education alive and well technic Institute in Troy NY If work that Conwell left behind For during times of financial difficulty alumni are involved in another way some Conwell s work remains as a They are absolutely essen- first it makes them more passionate memorial to her tial Thats the backbone of it all when they get to fund- raising s According to an article that said Charlotte Heartt director of Volunteer services offered by appeared in the Columbus Dispatch development at Smith College in alumni at various schools include Conwell and a friend Robert Scheid Northampton Mass recruiting serving on legislative were killed in Helena Ark while Statistics agree The 1991 committees to lobby state govern- their boat was moored for repairs Voluntary Support of Education ments serving on college steering Conwell had been sexually assulted survey published by the Council committees and other boards and I Both were stabbed
    [Show full text]
  • A Characterization of Concrete Quasitopoi by Injectivity
    Journal of Pure and Applied Algebra 68 (1990) l-9 North-Holland A CHARACTERIZATION OF CONCRETE QUASITOPOI BY INJECTIVITY J. ADAMEK Faculty of Electrical Engineering, Suchbdtarova 2, Praha 6, Czechoslovakia H. HERRLICH FeldhGuser Str. 69, 2804 Lilienthal, FRG Received 9 June 1986 To our friend Bernhard Banaschewski, who demonstrates convincingly that-contrary to popular belief-it is possible to simultaneously get older, more creative and forceful as a mathematician and live a good life as well Concrete quasitopoi are characterized as the injectives among concrete, finitely complete categories. Quasitopos hulls are shown to be the injective hulls. Introduction Banaschewski and Bruns [5] have characterized Mac Neille completions of posets as injective hulls in the category Pos. This result has been generalized in [6], [7] and [l l] to the quasicategory Cat(X) of concrete categories over the base-category X (and concrete functors over X): injective ejects of Cat(X) are precisely the initially complete categories, and in- jective hulls are the Mac Neille completions introduced in [7]. Injectivity of K means (here and below) that for each full embedding A + B, which is a mor- phism in the given quasicategory (here Cat(X)), each morphism A+K can be extended to a morphism B -+ K. If X is the one-morphism category, then Cat(X) is the quasicategory of partially ordered classes, and hence, the latter result is a direct generalization of that in [5]. Recently, injectivity has been studied in the quasicategory Cat,(X) of concrete categories over X having finite, concrete [preserved by the forgetful functor] products (and concrete functors, preserving finite products).
    [Show full text]