Introduction to Topology

Bert Mendelson

Table of contents :
Cover ……Page 1
Short title ……Page 2
Title page ……Page 3
Copyright ……Page 4
Preface ……Page 5
Contents ……Page 7
1 Introduction ……Page 10
2 Sets and subsets ……Page 13
3 Set operations: union, intersection, and complements ……Page 16
4 Indexed families of sets ……Page 19
5 Products of sets ……Page 22
6 Functions ……Page 24
7 Composition of functions and diagrams ……Page 29
8 Inverse functions ……Page 35
9 Restriction and extension of functions ……Page 38
1 Introduction ……Page 41
2 Metric spaces ……Page 42
3 Continuity ……Page 48
4 Open spheres and neighborhoods ……Page 53
5 Open sets ……Page 61
6 Limit points ……Page 65
7 Closed sets ……Page 69
8 Products ……Page 74
9 Subspaces ……Page 80
10 Equivalence of metric spaces ……Page 84
1 Introduction ……Page 92
2 Topological spaces ……Page 93
3 Neighborhoods and neighborhood spaces ……Page 97
4 Closure, interior, boundary ……Page 104
5 Functions, continuity, homeomorphism ……Page 112
6 Subspaces ……Page 117
7 Products ……Page 121
1 Introduction ……Page 125
2 Connectedness ……Page 126
3 Connectedness on the real line ……Page 131
4 Some applications of connectedness ……Page 134
5 Components and local connectedness ……Page 143
6 Arcwise connected topological spaces ……Page 147
7 Homotopic paths ……Page 153
8 Simple connectedness ……Page 162
1 Introduction ……Page 171
2 Compact topological spaces ……Page 172
3 Compact subsets of the real line ……Page 180
4 Products of compact spaces ……Page 183
5 Compact metric spaces ……Page 187
6 Compactness and the Bolzano-Weierstrass property ……Page 195
7 Identification topologies and spaces ……Page 202
Bibliography ……Page 220
Special Symbols ……Page 221
Index ……Page 224