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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | IIT Bombay |
The Syllabus
- Definition and examples of topological spaces, Examples of topological spaces, Basis for topology, Subspace Topology, Product Topology.
- Continuous maps, Continuity of addition and multiplication maps, ring of continuous functions, Continuous maps to a product, Projection from a point.
- Closed subsets, Closure, Joining continuous maps, Metric spaces, Connectedness.
- Connected components, Path connectedness.
- Connectedness of GL(n,R)^+, Connectedness of GL(n,C), SL(n,C), SL(n,R), Hausdorff topological spaces, Compactness.
- SO(n) is connected, Compact metric spaces, Lebesgue Number Lemma, Locally compact spaces.
- One point compactification, One point compactification (continued), Uniqueness of one point compatification, Quotient topology, Quotient topology on G/H.
- Grassmannian, Normal topological spaces, Urysohn’s Lemma, Tietze Extension Theorem, Regular and Second Countable spaces, Urysohn’s Metrization Theorem.
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