Intuitive Concepts in Elementary Topology.

by B.H. Arnold

An introduction to topology employing an informal and intuitive approach for students with a knowledge of elementary calculus. 0. Statements and Proofs in Mathematics; 0.1 Statements; 0.2 Proofs; 0.3 Mathematical Induction; 1. What is Topology?; 1.1 A Glance at Euclidean Geometry; 1.2 What is Topology?; 2. Networks and Maps; 2.1 Traversability of Networks; 2.2 Planar Networks; 2.3 The Four Color Problem; 3. Topological Equivalence in Three-Dimensional Space; 3.1 Topological Equivalence; 3.2 Classification of Surfaces; 4. Maps on a Sphere with Handle; 4.1 Introduction; 4.2 Simply Connected Sets; 4.3 Euler's Theorem; 4.4 The Seven Color Theorem on a Torus; 5. The Jordan Curve Theorem; 5.1 Introduction; 5.2 A Proof for the Case of a Polygon; 6. Sets; 6.1 Introduction; 6.2 Relations Involving Sets; 6.3 Operations Involving Sets; 7. Transformations; 7.1 Introduction; 7.2 Transformations between Arbitrary Sets; 7.3 Transformations Between Subsets of Three-Dimensional Euclidean Space; 7.4 The Index of a Transformation; 7.5 Applications of Indices of Transformations; 8. Spaces; 8.1 Introduction; 8.2 Metric Spaces; 8.3 Topological Spaces; 8.4 Connected Sets; 8.5 Compact Sets; 8.6 Complete Sets.

Genres: Mathematics

176 pages, Hardcover

First published July 19, 2011

Reviews

[Liquidlasagna · Rating 5 out of 5]

should be more ambitious books like this one

[Adam Hamilton · Rating 5 out of 5]

very helpful introduction.