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1 What Is Topology? 1 Euler's Theorem 10 2 New Surfaces 20 Orientability 25; Dimension 28; Two More Surfaces 31; The Klein Bottle 34 3 The Shortest Moebius Strip 40 4 The Conical Moebius Strip 50 5 The Klein Bottle 62 6 The Projective Plane 78 Symmetry 82 7 Map Coloring 108 8 Networks 120 The Koenigsberg Bridges 120; Betti Numbers 123; Knots 132 9 The Trial of the Punctured Torus 136 10 Continuity and Discreteness 149 The "Next Number" 149; Continuity 151; Neighborhoods 154; Limit Points 158 11 Sets 162 Valid or Merely True? 162; Venn Diagrams 164; Open and Closed Sets 174; Transformations 182; Mapping 188; Homotopy I92 In Conclusion 197 Appendix 200 Index 207
Copyright © 1996-2008 Alexander Bogomolny
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