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Course11110615974 lectures

An invitation to Topology

Prof. Indrava Roy · IMSc

Start with lecture 1 At NPTEL

Lectures

week-01

  1. mod01lec01 - Introduction to Topology Video
  2. mod01lec02 - Basic Set theory Video
  3. mod01lec03 - Mathematical Logic - Part 1 Video
  4. mod01lec04 - Mathematical Logic - Part 2 Video
  5. mod01lec05 - Functions Video
  6. mod01lec06 - Finite Sets - Part 1 Video
  7. mod01lec07 - Finite Sets - Part 2 Video
  8. mod01lec08 - Infinite Sets Video
  9. mod01lec09 - Infinite Sets and Axiom of Choice Video

week-02

  1. mod02lec10 - Definition of aTopology Video
  2. mod02lec11 - Examples of different topologies: Video
  3. mod02lec12 - Basis for a topology Video
  4. mod02lec13 - Various topologies on the real line Video
  5. mod02lec14 - Comparison of topologies - Part 1 : Finer and coarser topologies Video
  6. mod02lec15 - Comparison of topologies - Part 2: Comparing the various topologies on R Video
  7. mod02lec16 - Basis and Sub-basis for a topology Video

week-03

  1. mod03lec17 - Various topologies: the subspace topology Video
  2. mod02lec18 - The Product topology Video
  3. mod02lec19 - Topologies on arbitrary Cartesian products Video
  4. mod02lec20 - Metric topology - Part 1 Video
  5. mod03lec21 - Metric topology - Part 2 Video
  6. mod03lec22 - Metric topology - Part 3 Video

week-04

  1. mod04lec23 - Closed Sets Video
  2. mod04lec24 - Closure and Limit points Video
  3. mod04lec25 - Continuous functions Video
  4. mod04lec26 - Construction of continuous functions Video
  5. mod04lec27 - Continuous functions on metric spaces - Part 1 Video
  6. mod04lec28 - Continuous functions on metric spaces - Part 2 Video

week-05

  1. mod05lec29 - Connectedness Video
  2. mod05lec30 - Some conditions for Connectedness Video
  3. mod05lec31 - Connectedness of the Real Line Video
  4. mod05lec32 - Connectedness of a Linear Continuum Video
  5. mod05lec33 - The Intermediate Value Theorem Video

week-06

  1. mod06lec34 - Path-connectedness Video
  2. mod06lec35 - Connectedness does not imply Path-connectedness - Part 1 Video
  3. mod06lec36 - Connectedness does not imply Path-connectedness - Part 2 Video
  4. mod06lec37 - Connected and Path-connected Components Video
  5. mod06lec38 - Local connectedness and Local Path-connectedness Video

week-07

  1. mod07lec39 - Compactness Video
  2. mod07lec40 - Properties of compact spaces Video
  3. mod07lec41 - The Heine-Borel Theorem Video
  4. mod07lec42 - Tychonoff't theorem Video
  5. mod07lec43 - Proof of Tychonoff's theorem - Part 1 Video
  6. mod07lec44 - Proof of Tychonoff's theorem - Part 2 Video

week-08

  1. mod08lec45 - Compactness in metric spaces Video
  2. mod08lec46 - Lebesgue Number Lemma and the Uniform Continuity theorem Video
  3. mod08lec47 - Different Kinds of Compactness Video
  4. mod08lec48 - Equivalence of various compactness properties for Metric Spaces Video
  5. mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces Video

week-09

  1. mod09lec50 - Baire Spaces Video
  2. mod09lec51 - Properties and Examples of Baire Spaces Video
  3. mod09lec52 - The Baire Category Theorem Video
  4. mod09lec53 - Complete Metric Spaces and the Baire Category theorem - Part 1 Video
  5. mod09lec54 - Complete Metric Spaces and the Baire Category theorem - Part 2 Video
  6. mod09lec55 - Application of the Baire Category theorem Video

week-10

  1. mod10lec56 - Regular and Normal spaces Video
  2. mod10lec57 - Properties and examples of regular and normal spaces Video
  3. mod10lec58 - Urysohn's Lemma Video
  4. mod10lec59 - Proof of Urysohn's Lemma Video
  5. mod10lec60 - Tietze Extension theorem - Part 1 Video
  6. mod10lec61 - Tietze Extension theorem - Part 2 Video

week-11

  1. mod11lec62 - Compactness and Completeness in Metric spaces Video
  2. mod11lec63 - The space of continuous functions - Part 1 Video
  3. mod11lec64 - The space of continuous functions - Part 2 Video
  4. mod11lec65 - Equicontinuity Video
  5. mod11lec66 - Total boundedness and Equicontinuity - Part 1 Video
  6. mod11lec67 - Total boundedness and Equicontinuity - Part 2 Video

week-12

  1. mod12lec68 - Topology of compact convergence - Part 1 Video
  2. mod12lec69 - Topology of compact convergence - Part 2 Video
  3. mod12lec70 - Equicontinuity revisited - Part 1 Video
  4. mod12lec71 - Equicontinuity revisited - Part 2 Video
  5. mod12lec72 - Locally compact Hausdorff spaces Video
  6. mod12lec73 - The Arzelà - Ascoli theorem Video

Live Session

  1. Live Session 04-05-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IMSc
Department
Mathematics
Teacher
Prof. Indrava Roy
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
Who can watch
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