Topology Illustrated

Topology Illustrated

by Peter Saveliev

Hardcover

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Product Details

ISBN-13: 9781495188756
Publisher: Peter Saveliev
Publication date: 02/02/2016
Pages: 664
Product dimensions: 7.00(w) x 10.00(h) x 1.44(d)

About the Author

Dr. Saveliev is a professor of mathematics at Marshall University, Huntington WV, USA. He has been involved in research in algebraic topology and several other fields.

Table of 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

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