Introduction to 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.
Table of Content
- Introduction
- Topological Spaces
- Interior, Closure, and Boundary
- Creating New Topological Spaces
- Continuous Functions and Homeomorphisms
- Metric Spaces
- Connectedness
- Compactness
- Dynamical Systems and Chaos
- Homotopy and Degree Theory
- Fixed Point Theorems and Applications
- Embeddings
- Knots
- Graphs and Topology
- Manifolds and Cosmology
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Salient Features
- Theoretical and applied approach- the authors focus on the basic concepts of
- Intuitive and accessibly written text
- Rigorous presentation of the mathematics with intuitive descriptions and discussions to increase student understand.
- Examples of real world application keep students engrossed in the material
- Numerous figures allow students to visualize and understand the material presented
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