Contents Preface vii Notation xi Basic Definitions 1 Chapter 1. Graphs 5 §1. Topological and Geometric Properties of Graphs 5 §2. Homotopy Properties of Graphs 29 §3. Graph Invariants 47 Chapter 2. Topology in Euclidean Space 55 §1. Topology of Subsets of Euclidean Space 55 §2. Curves in the Plane 63 §3. The Brouwer Fixed Point Theorem and Sperner's Lemma 72 Chapter 3. Topological Spaces 87 §1. Elements of General Topology 87 §2. Simplicial Complexes 99 §3. CW-Complexes 117 §4. Constructions 130 Chapter 4. Two-Dimensional Surfaces, Coverings, Bundles, and Homotopy Groups 139 §1. Two-Dimensional Surfaces 139 §2. Coverings 149
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