- Topological spaces : Definition, examples; bases, sub-bases; product topology, subspace topology, metric topology, quotient topology, second countability and separability.
- Continuity : Continuous functions on topological spaces, homeomorphisms.
- Connectedness : Definition, example, path connectedness and local connectedness.
- Compactness : Definition, limit point compactness, sequential compactness, local compactness; Tychonoff theorem, Stone-Weierstrass theorem.
- Separation Axioms : Hausdorff, regular and normal spaces; Urysohn lemma and Tietze extension theorem; compactification.
- Metrizability : Urysohn metrization theorem.
- Algebraic Topology : Fundamental groups, examples; covering spaces.
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