Experiments in Topology

Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

1 What is Topology?
Euler's Theorem
2 New Surfaces
Orientability
Dimension
Two More Surfaces
The Klein Bottle
3 The Shortest Moebius Strip
4 The Conical Moebius Strip
5 The Klein Bottle
6 The Projective Plane
Symmetry
7 Map Coloring
8 Networks
The Koenigsberg Bridges
Betti Numbers
Knots
9 The Trial of the Punctured Torus
10 Continuity and Discreteness
"The "Next Number"
Continuity
Neighborhoods
Limit Points
11 Sets
Valid or Merely True?
Venn Diagrams
Open and Closed Sets
Transformations
Mapping
Homotopy
In Conclusion
Appendix
Index