ProofWiki:Books/Stephen Barr/Experiments in Topology

Stephen Barr: Experiments in Topology

Published 1964, Dover Publications, Inc..

ISBN 0-486-25933-1

Subject Matter

• Topology

Contents

• 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