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 very much material, just the most basic things.


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

Exercises