Experiments in Topology

Stephen Barr

	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
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