← Theoretical / proof-based

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In this program

Hausdorff spaces
Separation axioms (T0–T4 overview)
Limit points and derived sets
First- and second-countability
Metric spaces as topological spaces
Completeness in metric spaces (introduction)

Separation and countability

First- and second-countability

Introductory topology · Theoretical / proof-based

Topic

First- and second-countability; separable spaces

Practice by unit: Separation and countability

Undergraduate Introductory Topology — scope drawn from open topology notes (metric/topological spaces) and typical US intro topology syllabi.

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