← Theoretical / proof-based

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In this program

Topological spaces, bases, and subspaces
Continuity and homeomorphisms
Product topologies
Compactness: Heine–Borel, Tychonoff (introduction), sequential compactness
Connectedness and path connectedness

Point-set topology

Connectedness and path connectedness

Topology · Theoretical / proof-based

Topic

Connectedness and path connectedness

Practice by unit: Point-set topology

Graduate Topology — scope drawn from Bradley–Bryson–Terilla Topology (MIT Press open chapters) and typical graduate point-set / algebraic topology intro syllabi.

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