Topology through inquiry /
| Main Authors: | , |
|---|---|
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island :
MAA Press: an imprint of the American Mathematical Society,
[2019]
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| Series: | AMS/MAA textbooks ;
v. 58. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Preface: Four ways to use this book
- Introduction: The enchanting world of topology
- Cardinality : to infinity and beyond
- Topological spaces : fundamentals
- Bases, subspaces, products : creating new spaces
- Separation properties : separating this from that
- Countable features of spaces : size restrictions
- Compactness : the next best thing to being finite
- Continuity : when nearby points stay together
- Connectedness : when things don't fall into pieces
- Metric spaces : getting some distance
- Transition from point-set topology to algebraic and geometric topology : similar strategies, different domains
- Classification of 2-manifolds : organizing surfaces
- Fundamental group : capturing holes
- Covering spaces : layering it on
- Manifolds, simplexes, complexes, and triangulability : building blocks
- Simplicial Z₂-homology : physical algebra
- Applications of Z₂-homology : a topological superhero
- Simplicial Z-homology : getting oriented
- Singular homology : abstracting objects to maps
- The end : a beginning-reflections on topology and learning.