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Topology Illustrated

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Topology Illustrated by Peter Saveliev

View through quotient door manifold.png

The full text below.

Work in progress... If you have a question or a comment, drop me a line.

Note: Ignore the occasional links as you read the sections below. Instead, click Back when you are finished and continue to the next section.


CONTENTS


Preface 1

Chapter 1. Cycles and boundaries

  1. Topology around us 10
  2. Homology classes 15
  3. Topology of graphs 13
  4. Homology groups of graphs 17
  5. Maps of graphs 19

Chapter 2. Topologies

  1. The intrinsic definition of continuity 11
  2. Neighborhoods and topologies 12
  3. Topological spaces 15
  4. Continuous functions 22
  5. Subspaces 16

Chapter 3. Complexes

  1. The binary algebra of cells 21
  2. Cubical complexes 18
  3. The algebra of oriented cells 19
  4. Simplicial complexes 17
  5. Simplicial homology 19
  6. Simplicial maps 20

Chapter 4. Spaces

  1. Compact spaces 12
  2. Quotients 20
  3. Cell complexes 22
  4. Triangulations 17
  5. Manifolds 29
  6. Products 28

Chapter 5. Maps

  1. Homotopy 25
  2. Cell maps 23
  3. Maps of polyhedra 27
  4. The Euler and Lefschetz numbers 23
  5. Homology of parametric spaces 21


Appendix: Student's guide to proof writing 3

Appendix: Notation 4


Estimated:

  • 531 pages
  • 657 illustrations
  • 648 exercises


References

These are the books I've used for teaching in the past: