Topology Illustrated -- contents

Topology Illustrated by Peter Saveliev

CONTENTS

• Chapter 1. Cycles
  • 1. Topology around us
  • 2. Homology classes
  • 3. Topology of graphs
  • 4. Homology groups of graphs
  • 5. Maps of graphs
  • 6. Binary calculus on graphs

• Chapter 2. Topologies
  • 1. A new look at continuity
  • 2. Neighborhoods and topologies
  • 3. Topological spaces
  • 4. Continuous functions
  • 5. Subspaces

• Chapter 3. Complexes
  • 1. The algebra of cells
  • 2. Cubical complexes
  • 3. The algebra of oriented cells
  • 4. Simplicial complexes
  • 5. Simplicial homology
  • 6. Simplicial maps
  • 7. Parametric complexes

• Chapter 4. Spaces
  • 1. Compacta
  • 2. Quotients
  • 3. Cell complexes
  • 4. Triangulations
  • 5. Manifolds
  • 6. Products

• Chapter 5. Maps
  • 1. Homotopy
  • 2. Cell maps
  • 3. Maps of polyhedra
  • 4. The Euler and Lefschetz numbers
  • 5. Set-valued maps

• Chapter 6. Forms
  • 1. Discrete forms and cochains
  • 2. Calculus on cubical complexes
  • 3. Cohomology
  • 4. Metric tensor

• Chapter 7. Flows
  • 1. Metric complexes
  • 2. ODEs
  • 3. PDEs
  • 4. Social choice