Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Indrava Roy
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 73
NPTEL Course Size : 3.7 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Introduction to Topology
Lecture 2 - Basic Set theory
Lecture 3 - Mathematical Logic - Part 1
Lecture 4 - Mathematical Logic - Part 2
Lecture 5 - Functions
Lecture 6 - Finite Sets - Part 1
Lecture 7 - Finite Sets - Part 2
Lecture 8 - Infinite Sets
Lecture 9 - Infinite Sets and Axiom of Choice
Lecture 10 - Definition of aTopology
Lecture 11 - Examples of different topologies
Lecture 12 - Basis for a topology
Lecture 13 - Various topologies on the real line
Lecture 14 - Comparison of topologies - Part 1: Finer and coarser topologies
Lecture 15 - Comparison of topologies - Part 2: Comparing the various topologies on R
Lecture 16 - Basis and Sub-basis for a topology
Lecture 17 - Various topologies: the subspace topology
Lecture 18 - The Product topology
Lecture 19 - Topologies on arbitrary Cartesian products
Lecture 20 - Metric topology - Part 1
Lecture 21 - Metric topology - Part 2
Lecture 22 - Metric topology - Part 3
Lecture 23 - Closed Sets
Lecture 24 - Closure and Limit points
Lecture 25 - Continuous functions
Lecture 26 - Construction of continuous functions
Lecture 27 - Continuous functions on metric spaces - Part 1
Lecture 28 - Continuous functions on metric spaces - Part 2
Lecture 29 - Connectedness
Lecture 30 - Some conditions for Connectedness
Lecture 31 - Connectedness of the Real Line
Lecture 32 - Connectedness of a Linear Continuum
Lecture 33 - The Intermediate Value Theorem
Lecture 34 - Path-connectedness
Lecture 35 - Connectedness does not imply Path-connectedness - Part 1
Lecture 36 - Connectedness does not imply Path-connectedness - Part 2
Lecture 37 - Connected and Path-connected Components
Lecture 38 - Local connectedness and Local Path-connectedness
Lecture 39 - Compactness
Lecture 40 - Properties of compact spaces
Lecture 41 - The Heine-Borel Theorem
Lecture 42 - Tychonoff't theorem
Lecture 43 - Proof of Tychonoff's theorem - Part 1
Lecture 44 - Proof of Tychonoff's theorem - Part 2
Lecture 45 - Compactness in metric spaces
Lecture 46 - Lebesgue Number Lemma and the Uniform Continuity theorem
Lecture 47 - Different Kinds of Compactness
Lecture 48 - Equivalence of various compactness properties for Metric Spaces
Lecture 49 - Compactness and Sequential Compactness in arbitrary topological spaces
Lecture 50 - Baire Spaces
Lecture 51 - Properties and Examples of Baire Spaces
Lecture 52 - The Baire Category Theorem
Lecture 53 - Complete Metric Spaces and the Baire Category theorem - Part 1
Lecture 54 - Complete Metric Spaces and the Baire Category theorem - Part 2
Lecture 55 - Application of the Baire Category theorem
Lecture 56 - Regular and Normal spaces
Lecture 57 - Properties and examples of regular and normal spaces
Lecture 58 - Urysohn's Lemma
Lecture 59 - Proof of Urysohn's Lemma
Lecture 60 - Tietze Extension theorem - Part 1
Lecture 61 - Tietze Extension theorem - Part 2
Lecture 62 - Compactness and Completeness in Metric spaces
Lecture 63 - The space of continuous functions - Part 1
Lecture 64 - The space of continuous functions - Part 2
Lecture 65 - Equicontinuity
Lecture 66 - Total boundedness and Equicontinuity - Part 1
Lecture 67 - Total boundedness and Equicontinuity - Part 2
Lecture 68 - Topology of compact convergence - Part 1
Lecture 69 - Topology of compact convergence - Part 2
Lecture 70 - Equicontinuity revisited - Part 1
Lecture 71 - Equicontinuity revisited - Part 2
Lecture 72 - Locally compact Hausdorff spaces
Lecture 73 - The Arzelà - Ascoli theorem