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Notes on Introductory Point-Set Topology |
These are notes from the first part of an undergraduate course in 2005. There
are only about 50 pages, so they don't cover a lot of material, just the most
basic things. For example Urysohn's Lemma and the Tietze Extension Theorem are notable omissions.
Chapter 1. Basic Point-Set Topology
- Topological Spaces
- Interior, Closure, and Boundary
- Basis for a Topology
- Metric Spaces
- Subspaces
- Continuity and Homeomorphisms
- Product Spaces
- Exercises
Chapter 2. Connectedness
- Path-connected Spaces
- Cut Points
- Connected Components and Path Components
- The Cantor Set
- Exercises
Chapter 3. Compactness
- Compact Sets in Euclidean Space
- Hausdorff Spaces
- Normal Spaces
- Lebesgue Numbers
- Infinite Products
- Exercises
Chapter 4. Quotient Spaces
- The Quotient Topology
- Surfaces
- Exercises