# Pacific Math Club Lecture Series: Topology

Lecturer, *Pacific Math Club*, Spring 2024

Ran a weekly lecture series through University of the Pacific’s mathematics club to lecture on topics from point-set topology which is not offered as a course at the University of the Pacific. Topics were presented in a way friendly to those with background in calculus at the levels of MATH 051 and MATH 053.

## Resources used

Handouts written by myself that are inspired by or reference the following books:

**Real Mathematical Analysis**by Pugh**Introduction to Topological Manifolds**by Lee

## Topics Covered

- Real analysis in \(\mathbb R\) and \(\mathbb R^n\)
- Sequences, subsequences, and convergence
- \(\varepsilon\)-\(\delta\) condition
- Continuity

- Metric spaces
- Sequences, subsequences, and convergence
- \(\varepsilon\)-\(\delta\) condition
- Open subsets and closed subsets
- Continuity and homeomorpisms
- Metric subspaces and product spaces

- Topological spaces
- Topology and open subsets
- Sequences, subsequences, and convergence
- Continuity and homeomorphisms
- Hausdorff Property
- Bases and countability properties
- Manifolds
- Subspaces
- Product spaces
- Quotient spaces
- Compact spaces
- Connected spaces