Math 441 - Introductory Topology I
Description
Math 441 provides an introduction to topology, particularly point-set topology, which covers definitions from topology using the language of set theory.
Topics covered
Topics covered in Math 441 usually include:
- Topological spaces and construction of topological spaces
- Topological basis
- Order topology
- Product topology
- Subspace topology
- Metric spaces
- Quotient spaces
- Connectedness
- Path-connectedness
- Local connectedness and local path-connectedness
- Compactness
- Variants of compactness, including sequential compactness
- Countability and separation axioms
- Urysohn lemma
- Urysohn metrization theorem
- Tietze extension theorem
Note that the exact list of topics may vary by instructor and semester. Additional topics may include basic objects of algebraic topology, such as fundamental groups, and classification of surfaces.
Comments on prerequisites
There are some similarities and overlap between Math 411 and 441, so some people who have taken both courses encourage taking the courses concurrently if you plan to take both.
Resources
Textbook
The usual textbook for the class is Topology by James Munkres.
Additional materials
A previous course page from when the course was taught by Sam Spiro in Fall 2023, with some linked notes, may be found online at https://samspiro.xyz/Teaching/Classes/TopologyFA23.