Course Notes for Math 986

Point-Set Topology:

Section 1.1: Basic definitions and examples

Section 1.2: The subspace topology

Section 1.3: More key concepts

Section 1.4: Continuous functions

Section 1.5: Products of topological spaces

Section 1.6: Metric spaces

Section 1.7: Connected spaces

Section 1.8: Compact spaces

Section 1.9: Quotient spaces

Topological Groups:

Section 2.1: Topological groups

Section 2.2: Profinite groups

Section 2.3: Examples

Differentiable topology and de Rham cohomology:

Section 3.1: Motivation

Section 3.2: de Rham cohomology on Rⁿ

Section 3.3: Some general homological algebra