Theoretical / proof-based
Introductory topology · Undergraduate · Math
Topics
Topological spaces
- Topological spaces: definition and examples (Euclidean, discrete, cofinite)
- Open and closed sets; interior, closure, and boundary
- Bases and subbases; subspace topology
- Continuous functions and homeomorphisms
- Product and quotient topologies (introduction)
Separation and countability
- Hausdorff spaces and separation axioms (T0–T4 overview)
- Limit points and derived sets
- First- and second-countability; separable spaces
- Metric spaces as topological spaces; equivalence of definitions
- Completeness in metric spaces (introduction)
Compactness and connectedness
- Compactness: open covers and sequential compactness in metric spaces
- Heine–Borel and Bolzano–Weierstrass in R^n
- Connected and path-connected spaces; components
- Compactness of continuous images and extreme value theorem (topological proof)
- Introduction to homotopy and the fundamental group (preview)
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$1,162 · Introductory 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.