Introduction to Topology: Pure and Applied, 1st edition

Published by Pearson (June 18, 2007) © 2008

  • Colin Adams
  • Robert Franzosa
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  • A print text

For juniors, seniors, and graduate students of various majors, taking a first course in topology.

 

This book introduces topology as an important and fascinating mathematics discipline.   Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields.
  • 0. Introduction
  • 1. Topological Spaces
  • 2. Interior, Closure, and Boundary
  • 3. Creating New Topological Spaces
  • 4. Continuous Functions and Homeomorphisms
  • 5. Metric Spaces
  • 6. Connectedness
  • 7. Compactness
  • 8. Dynamical Systems and Chaos
  • 9. Homotopy and Degree Theory
  • 10. Fixed Point Theorems and Applications
  • 11. Embeddings
  • 12. Knots
  • 13. Graphs and Topology
  • 14. Manifolds and Cosmology

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