Main Subjects
Topology
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Major Courses
- Introduction to Algebraic Topology
- Set Theory, Relations, and Functions
- Metric spaces
- Interior/Boundary/limit points, closure
- Sequences, Convergence, and properties
- Completion, Compactness, and Connectedness of Metric Spaces.
- Compactness & Equivalent Conditions for Compact Metric Spaces
- Topological Spaces, Basis, subspaces, product topology
- Separation axioms, First and Second Countability, Baire space
- Compactness in general topological spaces, Continuity and compactness
- Subspace, Lebesgue covering lemma.
- Tube lemma and its application
- Metrizable spaces and hereditary properties of topological spaces.
- Product of Regular spaces, Connectedness.
- Quotient topology, quotient spaces, and Tychonoff theorem
- Topological equivalence
- Orientability
- Topology of surfaces
