Topology

General Topology

1. Topological Spacesopen sets, bases, subspace/order/product topologies6.5–12 h
2. Continuous Functions & Homeomorphismcharacterizations, embedding, topological equivalence6.5–12 h
3. Separation AxiomsT1, Hausdorff, regular, normal, Urysohn lemma6.5–12 h
4. Compactnessfinite subcover property, Tychonoff theorem (statement), Heine-Borel general6.5–12 h
5. Connectednesspath connectedness, components, intermediate value generalization6.5–12 h
6. Product & Quotient Spacesquotient maps, identification spaces, examples6.5–12 h

Algebraic Topology Foundations

1. Homotopy & Pathshomotopy of maps, fundamental group6.5–12 h
2. Computing Fundamental Groupspi1 of circle, van Kampen theorem intro, covering spaces intro6.5–12 h