Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-1978 Topological Properties of C(X, Y) Chris Alan Schwendiman Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mathematics Commons Recommended Citation Schwendiman, Chris Alan, "Topological Properties of C(X, Y)" (1978). All Graduate Theses and Dissertations. 6949. https://digitalcommons.usu.edu/etd/6949 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact
[email protected]. TOPOLOGICALPROPERTIES OF C(X,Y) by Chris Alan Schwendiman A thesis submitted in partial fulfillment of the requirements for the degree of MASTEROF SCIENCE in Mathematics Plan A Approved: UTAHSTATE UNIVERSITY Logan, Utah 1978 ACKNOWLEDGEMENTS I wish to express my many thanks to the members of my committee for their time and effort which they have given me. Their assistance and patience were invaluable in the preparation of this thesis. In particular, I would like to give special thanks to Dr. E. R. Heal who made it possible to study this interesting topic. Chris A. Schwendiman TABLE OF CONTENTS INTRODUCTION. 1 PRELIMIN ARIES 2 PROPERTIES OF C(X,Y) WHENXIS COMPACT 11 PROPERTIES OF C(X,Y) WHENX MAYNOT BE COMPACT 14 REFERENCES 22 VITA 23 ABSTRACT Topological Properties of C(X,Y) by Chris A. Schwendiman, Master of Science Utah State University, 1978 Major Professor: Dr. E. Robert Heal Department: Mathematics The purpose of this paper is to examine the important topological properties of the function spaces BC(X,Y) and C(X,Y).