B. H. Arnold

Indeholder "Preface", "zero: Statements and Proofs in Mathematics", " 0.1 Statements", " 0.2 Proofs", " 0.3 Mathematical Induction", "one: What is Topology?", " 1.1 A Glance at Euclidean Geometry", " 1.2 What is Topology?", "two: Networks and Maps", " 2.1 Traversability of Networks", " 2.2 Planar Networks", " 2.3 The Four Color Problem", "three: Topological Equivalence in Three-Dimensional Space", " 3.1 Topological Equivalence", " 3.2 Classification of Surfaces", "four: Maps on a Sphere with Handles", " 4.1 Introduction", " 4.2 Simply Connected Sets", " 4.3 Euler's Theorem", " 4.4 The Seven Color Theorem on a Torus", "five: The Jordan Curve Theorem", " 5.1 Introduction", " 5.2 A Proof for the Case of a Polygon", "six: Sets", " 6.1 Introduction", " 6.2 Relations Involving Sets", " 6.3 Operations Involving Sets", "seven: 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", "eight: Spaces", " 8.1 Introduction", " 8.2 Metric Spaces", " 8.3 Topological Spaces", " 8.4 Connected Sets", " 8.5 Compact Sets", " 8.6 Complete Sets", "References", "Index".

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