Open, Closed, and Compact Sets
Part 1 - Introduction and Open Sets in Metric Spaces
Part 2 - Topological Spaces
Part 3 - Closed Sets and Closure
Part 4 - Compact Sets
Part 5 - Closed Subsets of Compact Sets are Compact
Locally Compact Hausdorff Spaces
Part 6 - Hausdorff Spaces
Part 7 - Compact Sets are Closed
Part 8 - Locally Compact Hausdorff Spaces
Part 9 - Continuity and Semicontinuity
Part 10 - Compact Sets Stay Compact Under Continuous Maps
Part 11 - Urysohn’s Lemma
Part 12 - Intermediate Compact and Open Sets
Part 13 - Proof of Urysohn’s Lemma
Part 14 - Partition of Unity
Connectedness
Part 15 - Connected Spaces
Part 16 - Path-Connected Spaces
Part 17 - Locally Path-Connected Spaces
Part 18 - Path-Connected Components