Book:Bert Mendelson/Introduction to Topology/Third Edition

From ProofWiki
Jump to navigation Jump to search

Bert Mendelson: Introduction to Topology (3rd Edition)

Published $\text {1975}$, Dover Publications, Inc.

ISBN 0-486-66352-3.

Subject Matter


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


Further Editions

Source work progress

Got bogged down in Neighborhood Spaces, and I have basically skipped the exercises. Reworking, getting the edition correct:
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: