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1 Theory of Sets
1 Introduction
2 Sets and subsets
3 "Set operations: union, intersection, and complement"
4 Indexed families of sets
5 Products of sets
6 Functions
7 Relations
8 Composition of functions and diagrams
9 "Inverse functions, extensions, and restrictions"
10 Arbitrary products
2 Metric Spaces
1 Introduction
2 Metric spaces
3 Continuity
4 Open balls and neighborhoods
5 Limits
6 Open sets and closed sets
7 Subspaces and equivalence of metric spaces
8 An infinite dimensional Euclidean space
3 Topological Spaces
1 Introduction
2 Topological spaces
3 Neighborhoods and neighborhood spaces
4 "Closure, interior, boundary"
5 "Functions, continuity, homeomorphism"
6 Subspaces
7 Products
8 Identification topologies
9 Categories and functors
4 Connectedness
1 Introduction
2 Connectedness
3 Connectedness on the real line
4 Some applications of connectedness
5 Components and local connectedness
6 Path-connected topological spaces
7 Homotopic paths and the fundamental group
8 Simple connectedness
5 Compactness
1 Introduction
2 Compact topological spaces
3 Compact subsets of the real line
4 Products of compact spaces
5 Compact metric spaces
6 Compactness and the Bolzano-Weierstrass property
7 Surfaces by identification
Bibliography
Index
1 Theory of Sets
1 Introduction
2 Sets and subsets
3 "Set operations: union, intersection, and complement"
4 Indexed families of sets
5 Products of sets
6 Functions
7 Relations
8 Composition of functions and diagrams
9 "Inverse functions, extensions, and restrictions"
10 Arbitrary products
2 Metric Spaces
1 Introduction
2 Metric spaces
3 Continuity
4 Open balls and neighborhoods
5 Limits
6 Open sets and closed sets
7 Subspaces and equivalence of metric spaces
8 An infinite dimensional Euclidean space
3 Topological Spaces
1 Introduction
2 Topological spaces
3 Neighborhoods and neighborhood spaces
4 "Closure, interior, boundary"
5 "Functions, continuity, homeomorphism"
6 Subspaces
7 Products
8 Identification topologies
9 Categories and functors
4 Connectedness
1 Introduction
2 Connectedness
3 Connectedness on the real line
4 Some applications of connectedness
5 Components and local connectedness
6 Path-connected topological spaces
7 Homotopic paths and the fundamental group
8 Simple connectedness
5 Compactness
1 Introduction
2 Compact topological spaces
3 Compact subsets of the real line
4 Products of compact spaces
5 Compact metric spaces
6 Compactness and the Bolzano-Weierstrass property
7 Surfaces by identification
Bibliography
Index
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