Book:Bert Mendelson/Introduction to Topology/Third Edition

Subject Matter

 * Topology

Contents

 * Preface to Third Edition


 * $1 \quad$ 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


 * $2 \quad$ 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


 * $3 \quad$ 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 of topologies
 * 9 Categories and functors


 * $4 \quad$ 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


 * $5 \quad$ 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



Source work progress
* : $\S 3.3$: Neighborhoods and Neighborhood Spaces: Exercise $3$
 * Got bogged down in Neighborhood Spaces, and I have basically skipped the exercises. Reworking:


 * : Chapter $1$: Theory of Sets: $\S 10$: Arbitrary Products: Exercise $1$
 * Work needed on establishing rigorous definitions and understandable interpretations of a general cartesian product of a family of sets indexed by an uncountable set.

Revisit the following -- it has been glossed over:


 * : Chapter $1$: Theory of Sets: $\S 7$: Relations: Exercise $2$


 * Rechecked again, satisfactory now up to here:


 * : Chapter $1$: Theory of Sets: $\S 5$: Products of Sets: Exercise $3$