Introduction to Topology

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