Introduction to topology / Bert Mendelson.

Contents

Preface
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

Includes bibliographical references and index.