Lecture 1 of 42Week 1
Lecture 1.1: Definition and examples of topological spaces
Prof. Ronnie Sebastian · IIT Bombay
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- Point Set Topology, IIT Bombay (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Lecture 1.1: Definition and examples of topological spaces
- Lecture 1.2: Examples of topological spaces
- Lecture 1.3: Basis for topology
- Lecture 1.4: Subspace Topology
- Lecture 1.5: Product Topology
- Lecture 2.1: Product Topology (continued)
- Lecture 2.2: Continuous maps
- Lecture 2.3: Continuity of addition and multiplication maps
- Lecture 2.4: Continuous maps to a product
- Lecture 2.5: Projection from a point
- Lecture 3.1: Closed subsets
- Lecture 3.2: Closure
- Lecture 3.3: Joining continuous maps
- Lecture 3.4: Metric spaces
- Lecture 3.5: Connectedness
- Lecture 4.1: Connectedness (continued)
- Lecture 4.2: Connectedness (continued)
- Lecture 4.3: Connected components
- Lecture 4.4: Path connectedness
- Lecture 4.5: Path connectedness (continued)
- Lecture 5.1: Connectedness of GL(n,R)^+ (math symbol)
- Lecture 5.2: Connectedness of GL(n,C), SL(n,C), SL(n,R)
- Lecture 5.3: Compactness
- Lecture 5.4: Compactness (continued)
- Lecture 5.5: Compactness (continued)
- Lecture 6.1: Compactness (continued)
- Lecture 6.2: SO(n) is connected
- Lecture 6.3: Compact metric spaces
- Lecture 6.4: Lebesgue Number Lemma
- Lecture 6.5: Locally compact spaces
- Lecture 7.1: One point compactification
- Lecture 7.2: One point compactification (continued)
- Lecture 7.3: Uniqueness of one point compatification
- Lecture 7.4: Quotient topology
- Lecture 7.5: Quotient topology on G/H
- Lecture 7.6: Grassmannian
- Lecture 8.1: Normal topological spaces
- Lecture 8.2: Urysohn’s Lemma
- Lecture 8.3: Tietze Extension Theorem
- Lecture 8.4: Regular and Second Countable spaces
- Lecture 8.5: Product Topology on \mathbb{R}^{\mathbb{N}}
- Lecture 8.6: Urysohn’s Metrization Theorem