Topological Properties of Spaces of Continuous Functions
This book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies studied are the set-open topologies and the uniform topolo
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1315 Robert A. McCoy Ibula Ntantu
Topological Properties of Spaces of Continuous Functions
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Authors
Robert A. McCoy Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, VA 24061, USA Ibula Ntantu Department of Mathematics Middle Tennessee State University Murfreesboro, TN 37132, USA
Mathematics Subject Classification (1980): 54C35, 54099, 54E99
ISBN 3-540-19302-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-19302-2 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
TABLE OF CONTENTS
Page INTRODUCTION
.
1
1. FUNCTION SPACE TOPOLOGIES
.
3
1.
Set-open Topologies
.
3
2.
Uniform Topologies
.
7
3.
Exercises and Problems..............................................................................
13
NATURAL FUNCTIONS.........................................................................................................
15
1.
Injections and Diagonal Functions...........................................................
15
2.
Composition Functions and Induced Functions...................................
16
3.
Evaluation Functions.....................................................................................
23
4.
Product Functions and Sum Functions..................................................
26
5.
Exponential Functions..................................................................................
30
6.
Exercises and Problems..............................................................................
35
II.
III.
IV.
CONVERGENCE AND COMPACT SUBSETS
,....
39
1.
Convergence.....................................................................................................
39
2.
Compact Subsets............................................................................................
43
3.
Exercises and Problems.............................................................................
47
CARDINAL FUNCTIONS.....................................................................................................
51
1.
Netweight..........................................................................................................
51
2.
Density and Cellularity..............................................................................
53
3.
Pseudoch
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