Introduction to Metric and Topological Spaces

Couverture
Clarendon Press, 1975 - 181 pages
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This book introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces. The book is aimed primarily at the second-year mathematics student, and numerous exercises are included.
 

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Table des matières

METRIC SPACES
19
TOPOLOGICAL SPACES
45
THE HAUSDORFF CONDITION
72
CONNECTED SPACES
93
CONVERGENCE
108
UNIFORM CONVERGENCE
114
COMPLETE METRIC SPACES
123
CRITERIA FOR COMPACTNESS
139
APPENDIX
149
GUIDE TO EXERCISES
160
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