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Bibliography The bibliography of this book is intended to reflect the state of the art of modern Cp-theory; besides, it is obligatory to mention the work of all authors whose results, in one form or another, are cited here. The bibliographic selection for this volume has 400 items to solve the proportional part of the task. ALAS,O.T. [1978] Normal and function spaces, Topology, Vol. II, Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam, 1980, 29–33. ALAS, O.T., GARCIA-FERREIRA,S.,TOMITA,A.H. [1999] The extraresolvability of some function spaces, Glas. Mat. Ser. III 34(54):1(1999), 23–35. ALAS, O.T., TAMARIZ-MASCARÚA,A. [2006] On the Cechˇ number of Cp .X/ II, Questions Answers Gen. Topology 24:1(2006), 31–49. ALSTER,K. [1979] Some remarks on Eberlein compacta, Fund. Math., 104:1(1979), 43–46. ALSTER,K.,POL,R. [1980] On function spaces of compact subspaces of ˙-products of the real line, Fund. Math., 107:2(1980), 135–143. AMIR,D.,LINDENSTRAUSS,J. [1968] The structure of weakly compact sets in Banach spaces, Annals Math., 88:1(1968), 35–46. ANDERSON,B.D. [1973] Projections and extension maps in C.T/, Illinois J. Math., 17(1973), 513–517. ARGYROS,S.,MERCOURAKIS,S.,NEGREPONTIS,S. [1983] Analytic properties of Corson compact spaces, General Topology and Its Rela- tions to Modern Analysis and Algebra, 5. Berlin, 1983, 12–24. ARGYROS,S.,NEGREPONTIS,S. [1983] On weakly K-countably determined spaces of continuous functions, Proc. Amer. Math. Soc., 87:4(1983), 731–736. © Springer International Publishing Switzerland 2015 493 V.V. Tkachuk, A Cp-Theory Problem Book, Problem Books in Mathematics, DOI 10.1007/978-3-319-16092-4 494 Bibliography ARHANGEL’SKII,A.V. [1959] An addition theorem for the weight of sets lying in bicompacta (in Russian), DAN SSSR, 126(1959), 239–241. [1976] On some topological spaces occurring in functional analysis (in Russian),Uspehi Mat. Nauk, 31:5(1976), 17–32. [1978a] On spaces of continuous functions with the topology of pointwise convergence (in Russian), Doklady AN SSSR, 240:3(1978), 506–508. [1978b] The structure and classification of topological spaces and cardinal invariants (in Russian), Uspehi Mat. Nauk, 33:6(1978), 29–84. [1981] Classes of topological groups (in Russian), Uspehi Mat. Nauk, 36:3(1981), 127–146. [1982c] Factorization theorems and function spaces: stability and monolithity (in Rus- sian), Doklady AN SSSR, 265:5(1982), 1039–1043. [1983c] Functional tightness, Q-spaces and -embeddings, Comment. Math. Univ. Car- olinae, 24:1(1983), 105–120. [1984b] Continuous mappings, factorization theorems and function spaces (in Russian), Trudy Mosk. Mat. Obsch., 47(1984), 3–21. [1985] Function spaces with the topology of pointwise convergence (in Russian), General Topology: Function Spaces and Dimension (in Russian), Moscow University P.H., 1985, 3–66. [1986] Hurewicz spaces, analytic sets and fan tightness of function spaces (in Russian), Doklady AN SSSR, 287:3(1986), 525–528. [1987] AsurveyofCp -theory, Questions and Answers in General Topology, 5(1987), 1–109. [1988a] Some results and problems in Cp .X/-theory. General Topology and Its Relations to Modern Analysis and Algebra, VI, Heldermann Verlag, Berlin, 1988, 11–31. [1989a] Topological Function Spaces (in Russian), Moscow University P.H., Moscow, 1989. [1989c] On iterated function spaces, Bull. Acad. Sci. Georgian SSR, 134:3(1989), 481–483. [1990a] Problems in Cp-theory, in: Open Problems in Topology, North Holland, Amster- dam, 1990, 603–615. [1990b] On the Lindelöf degree of topological spaces of functions, and on embeddings into Cp.X/, Moscow University Math. Bull., 45:5(1990), 43–45. [1992a] Topological Function Spaces (translated from Russian), Kluwer Academic Pub- lishers, Dordrecht, 1992. [1992b] Cp-theory, in: Recent Progress in General Topology, North Holland, Amsterdam, 1992, 1–56. [1995a] Spaces of mappings and rings of continuous functions, in: General Topology, 3, Encyclopedia Math. Sci., Springer, Berlin, 51(1995), 73–156. [1995b] A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolinae, 36:2(1995), 303–325. [1996a] On Lindelöf property and spread in Cp-theory, Topol. and Its Appl., 74: (1-3)(1996), 83–90. [1996b] On spread and condensations, Proc. Amer. Math. Soc., 124:11(1996), 3519–3527. [1997] On a theorem of Grothendieck in Cp-theory, Topology Appl. 80(1997), 21–41. [1998a] Some observations on Cp -theory and bibliography, Topology Appl., 89(1998), 203–221. [1998b] Embeddings in Cp-spaces, Topology Appl., 85(1998), 9–33. Bibliography 495 [2000a] On condensations of Cp-spaces onto compacta, Proc. Amer. Math. Soc., 128:6(2000), 1881–1883. [2000b] Projective -compactness, !1-caliber and Cp -spaces, Topology Appl., 104(2000), 13–26. ARHANGEL’SKII, A.V., CALBRIX,J. [1999] A characterization of -compactness of a cosmic space X by means of subspaces of RX , Proc. Amer. Math. Soc., 127:8(1999), 2497–2504. ARHANGEL’SKII, A.V., CHOBAN M.M. [1988] The extension property of Tychonoff spaces and generalized retracts, Comptes Rendus Acad. Bulg. Sci., 41:12(1988), 5–7. [1989] Cp.X/ and some other functors in general topology. Continuous extenders, Categorical Topology, World Scientific, London, 1989, 432–445. [1990] On the position of a subspace in the whole space, Comptes Rendus Acad. Bulg. Sci., 43:4(1990), 13–15. [1992] Extenders of Kuratowski–van Douwen and classes of spaces, Comptes Rendus Acad. Bulg. Sci., 45:1(1992), 5–7. [1996] On continuous mappings of Cp-spaces and extenders, Proc. Steklov Institute Math., 212(1996), 28–31. ARHANGEL’SKII, A.V., OKUNEV,O.G. [1985] Characterization of properties of spaces by properties of their continuous images (in Russian) Vestnik Mosk. Univ., Math., Mech., 40:5(1985), 28–30. ARHANGEL’SKII, A.V., PAV LOV,O.I. [2002] A note on condensations of Cp.X/ onto compacta, Comment. Math. Univ. Carolinae, 43:3(2002), 485–492. ARHANGEL’SKII, A.V., PONOMAREV,V.I. [1974] Basics of General Topology in Problems and Exercises (in Russian), Nauka, Moscow, 1974. ARHANGEL’SKII, A.V., SHAKHMATOV,D.B. [1988] On pointwise approximation of arbitrary functions by countable families of continuous functions (in Russian), Trudy Sem. Petrovsky, 13(1988), 206–227. ARHANGEL’SKII, A.V., SZEPTYCKI,P.J. [1997] Tightness in compact subspaces of Cp -spaces, Houston J. Math., 23:1(1997), 1–7. ARHANGEL’SKII, A.V., TKACHUK,V.V. [1985] Function Spaces and Topological Invariants (in Russian), Moscow University P.H., Moscow, 1985. [1986] Calibers and point-finite cellularity of the spaces Cp.X/ and some questions of S. Gul’ko and M. Hušek, Topology Appl., 23:1(1986), 65–74. ARHANGEL’SKII, A.V., USPENSKIJ,V.V. [1986] On the cardinality of Lindelöf subspaces of function spaces, Comment. Math. Univ. Carolinae, 27:4(1986), 673–676. ASANOV,M.O. [1979] On cardinal invariants of spaces of continuous functions (in Russian), Modern Topology and Set Theory (in Russian), Izhevsk, 1979, N 2, 8–12. [1980] On spaces of continuous maps, Izvestiia Vuzov, Mat., 1980, N 4, 6–10. [1983] About the space of continuous functions, Colloq. Math. Soc. Janos Bolyai, 41(1983), 31–34. 496 Bibliography ASANOV, M.O., SHAMGUNOV,N.K. [1981] The topological proof of the Nachbin–Shirota’s theorem, Comment. Math. Univ. Carolinae, 24:4(1983), 693–699. ASANOV, M.O., VELICHKO,M.V. [1981] Compact sets in Cp.X/ (in Russian), Comment. Math. Univ. Carolinae, 22:2(1981), 255–266. BANACH,T.,CAUTY,R. [1997] Universalité forte pour les sous-ensembles totalement bornés. Applications aux espaces Cp.X/, Colloq. Math., 73(1997), 25–33. BANDLOW,I. [1991] A characterization of Corson compact spaces, Commentationes Math. Univ. Carolinae, 32:3(1991), 545–550. [1994] On function spaces of Corson–compact spaces, Comment. Math. Univ. Caroli- nae, 35:2(1994), 347–356. BATUROV D.P. [1987] On subspaces of function spaces (in Russian), Vestnik Moskovsk. Univ., Math., Mech., 42:4(1987), 66–69. [1988] Normality of dense subsets of function spaces, Vestnik Moskovsk. Univ., Math., Mech., 43:4(1988), 63–65. [1990a] Normality in dense subspaces of products, Topology Appl., 36(1990), 111–116. [1990b] Some properties of the weak topology of Banach spaces, Vestnik Mosk. Univ., Math., Mech., 45:6(1990), 68–70. BELL,M.,MARCISZEWSKI,W. [2004] Function spaces on t-Corson compacta and tightness of polyadic spaces, Czech. Math. J., 54(129)(2004), 899–914. BELLA,A.,YASCHENKO,I.V. [1999] On AP and WAP spaces, Comment. Math. Univ. Carolinae, 40:3(1999), 531–536. BENYAMINI,Y.,RUDIN, M.E., WAGE,M. [1977] Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math- ematics, 70:2(1977), 309–324. BENYAMINI,Y.,STARBIRD,T. [1976] Embedding weakly compact sets into Hilbert space, Israel J. Math., 23(1976), 137–141. BESSAGA,C.,PELCZINSKI,A. [1960] Spaces of continuous functions, 4, Studia Math., 19(1960), 53–62. [1975] Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa, 1975. BLASKO,J.L. [1977] On -spaces and kR -spaces, Proc.Amer.Math.Soc.,67:1(1977), 179–186. [1990] The Gı -topology and K-analytic spaces without perfect compact sets, Colloq. Math., 58(1990), 189–199. BORGES,C.J. [1966a] On stratifiable spaces, Pacific J. Math., 17:1(1966), 1–16. [1966b] On function spaces of stratifiable spaces and compact spaces, Proc. Amer. Math. Soc., 17(1966), 1074–1078. Bibliography 497 BOURGAIN,J. [1977] Compact sets of the first Baire class, Bull. Soc. Math. Belg., 29:2(1977), 135–143. [1978] Some remarks on compact sets of first Baire class, Bull. Soc. Math. Belg., 30(1978), 3–10. BOURGAIN,J.,FREMLIN, D.H., TALAGRAND,M. [1978] Pointwise compact sets of Baire-measurable functions, Amer.J.Math., 100(1978), 845–886.
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  • On Countably Compact Topologies on Compact Groups and on Dyadic Compacta

    On Countably Compact Topologies on Compact Groups and on Dyadic Compacta

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector TOPOLOGY AND ITS APPLICATIONS ELSEVIER Topology and its Applications 57 (1994) 163-181 On countably compact topologies on compact groups and on dyadic compacta A.V. Arhangel’skii a,b a Department of Mathematics, Moscow State Vniversiiy, Moscow 119899, Russia ’ Department of Mathematics, Ohio University, Athens, OH, USA (Received 11 December 1992; revised 14 January 1993,6 September 1993) Abstract In this paper we apply certain classical results of S. Mazur, J. Keisler, A. Tarski and N.Th. Varopoulos to the theory of countably compact topological groups. For example, under a mild restriction on the cardinality of a compact group G, it is proved that there is no strictly stronger countably compact group topology on G. If f is a one-to-one continuous mapping of a countably compact topological group of countable tightness onto a compact Hausdorff space X, then X is metrizable. If a countably compact topological group of countable tightness acts continuously and transitively on a compact Hausdorff space X, then X is metrizable. Among the questions left unsettled is this: Let f be a sequentially continuous homomor- phism of a compact topological group G onto a topological group H. Is then H countably compact? Equivalently, is then H totally bounded? Under Martin’s axiom this question is answered positively. Key words: Countably compact group; Totally bounded group; Quotient mapping; Sequen- tially continuous mapping; Ulam measurable cardinal; Sequential cardinal AMS (MOS) Subj. Class.: 54AQ.5, 2OK45, 22CO5 In terminology we follow [1,7,8].