This site contains mathematics courses and book drafts and provides image analysis software. Created and run by Peter Saveliev.

# Topology Illustrated

### From Intelligent Perception

*Topology Illustrated* by Peter Saveliev

The full text of the ongoing draft is below. The book is about *homology*.

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**

- Topology around us 10
- Homology classes 15
- Topology of graphs 13
- Homology groups of graphs 17
- Maps of graphs 19

**Chapter 2. Topologies**

- The intrinsic definition of continuity 11
- Neighborhoods and topologies 13
- Topological spaces 15
- Continuous functions 24
- Subspaces 20

**Chapter 3. Complexes**

- The binary algebra of cells 21
- Cubical complexes 19
- The algebra of oriented cells 19
- Simplicial complexes 21
- Simplicial homology 19
- Simplicial maps 24
- Parametric complexes 21

**Chapter 4. Spaces**

- Compact spaces 12
- Quotients 20
- Cell complexes 22
- Triangulations 17
- Manifolds 29
- Products 28

**Chapter 5. Maps**

- Homotopy 27
- Cell maps 25
- Maps of polyhedra 27
- Euler and Lefschetz numbers 16
- Set-valued maps 15

Appendix: Student's guide to proof writing 3

Appendix: Notation 4

Estimated:

- 549 pages
- 701 illustrations
- 702 exercises

**References**

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