A first course in topology : continuity and dimension /
"How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society,
©2006.
|
| Series: | Student mathematical library ;
v. 31. |
| Subjects: |
Table of Contents:
- Introduction
- ch. 1. A little set theory
- Equivalence relations
- The Schröder-Berrnstein theorem
- The problem of invariance of dimension
- ch. 2. Metric and topological spaces
- Continuity
- ch. 3. Geometric notions
- ch. 4. Building new spaces from old
- Subspaces
- Products
- Quotients
- ch. 5. Connectedness
- Path-connectedness
- ch. 6. Compactness
- ch. 7. Homotopy and the fundamental group
- ch. 8. Computations and covering spaces
- ch. 9. The Jordan curve theorem
- Gratings and arcs
- The index of a point not on a Jordan curve
- A proof of the Jordan curve theorem
- ch. 10. Simplicial complexes
- Simplicial mappings and barycentric subdivision
- ch. 11. Homology
- Homology and simplicial mappings
- Topological invariance
- Where from here?
- Bibliography
- Notation index
- Subject index.