Includes bibliographical references (pages 244-245) and index.

1. Introduction -- 1.1 Euler's theorem -- 1.2 Topological equivalence -- 1.3 Surfaces -- 1.4 Abstract spaces -- 1.5 A classification theorem -- 1.6 Topological invariants -- 2. Continuity -- 2.1 Open and closed sets -- 2.2 Continuous functions -- 2.3 A space-filling curve -- 2.4 The Tietze extension theorem -- 3. Compactness and connectedness -- 3.1 Closed bounded subsets of E[n] -- 3.2 The Heine-Borel theorem -- 3.3 Properties of compact spaces -- 3.4 Product spaces -- 3.5 Connectedness -- 3.6 Joining points by paths -- 4. Identification spaces -- 4.1 Constructing a Möbius strip -- 4.2 The identification topology -- 4.3 Topological groups -- 4.4 Orbit spaces -- 5. The fundamental group -- 5.1 Homotopic maps -- 5.2 Construction of the fundamental group -- 5.3 Calculations -- 5.4 Homotopy type -- 5.5 The Brouwer fixed-point theorem -- 5.6 Separation of the plane -- 5.7 The boundary of a surface -- 6. Triangulations -- 6.1 Triangulating spaces -- 6.2 Barycentric subdivision -- 6.3 Simplicial approximation -- 6.4 The edge group of a complex -- 6.5 Triangulating orbit spaces -- 6.6 Infinite complexes -- 7. Surfaces -- 7.1 Classification -- 7.2 Triangulation and orientation -- 7.3 Euler characteristics -- 7.4 Surgery -- 7.5 Surface symbols -- 8. Simplicial homology -- 8.1 Cycles and boundaries -- 8.2 Homology groups -- 8.3 Examples -- 8.4 Simplicial maps -- 8.5 Stellar subdivision -- 8.6 Invariance -- 9. Degree and Lefschetz number -- 9.1 Maps of spheres -- 9.2 The Euler-Poincaré formula -- 9.3 The Borsuk-Ulam theorem -- 9.4 The Lefschetz fixed-point theorem -- 9.5 Dimension -- 10. Knots and covering spaces -- 10.1 Examples of knots -- 10.2 The knot group -- 10.3 Seifert surfaces -- 10.4 Covering spaces -- 10.5 The Alexander polynomial -- Appendix: Generators and relations.

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