Introduction to topology : pure and applied
著者
書誌事項
Introduction to topology : pure and applied
Pearson Education, Pearson Prentice Hall, c2008
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注記
Includes bibliographical reference and index
内容説明・目次
内容説明
For juniors and seniors 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.
目次
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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