Theoretical / proof-based
Topology · Graduate · Math
Topics
Point-set topology
- Topological spaces, bases, and subspaces
- Continuity, homeomorphisms, and product topologies
- Compactness: Heine–Borel, Tychonoff (introduction), sequential compactness
- Connectedness and path connectedness
Separation and countability
- Hausdorff, regular, and normal spaces (introduction)
- Urysohn lemma and Tietze extension (as covered)
- First and second countability
Algebraic topology introduction
- Homotopy and homotopy equivalence
- Fundamental group: computation and Van Kampen theorem (introduction)
- Covering spaces (overview)
Manifolds and geometry intro
- Topological and smooth manifolds (definitions and examples)
- Tangent spaces and vector fields (introduction)
- Orientation and degree (overview)
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$1,162 · Topology · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.