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NOC:An invitation to Topology (Video)
Syllabus
Co-ordinated by :
IIT Madras
Available from :
2021-10-28
Lec :
1
Modules / Lectures
Intro Video
week-01
mod01lec01 - Introduction to Topology
mod01lec02 - Basic Set theory
mod01lec03 - Mathematical Logic - Part 1
mod01lec04 - Mathematical Logic - Part 2
mod01lec05 - Functions
mod01lec06 - Finite Sets - Part 1
mod01lec07 - Finite Sets - Part 2
mod01lec08 - Infinite Sets
mod01lec09 - Infinite Sets and Axiom of Choice
week-02
mod02lec10 - Definition of aTopology
mod02lec11 - Examples of different topologies:
mod02lec12 - Basis for a topology
mod02lec13 - Various topologies on the real line
mod02lec14 - Comparison of topologies - Part 1 : Finer and coarser topologies
mod02lec15 - Comparison of topologies - Part 2: Comparing the various topologies on R
mod02lec16 - Basis and Sub-basis for a topology
week-03
mod03lec17 - Various topologies: the subspace topology
mod02lec18 - The Product topology
mod02lec19 - Topologies on arbitrary Cartesian products
mod02lec20 - Metric topology - Part 1
mod03lec21 - Metric topology - Part 2
mod03lec22 - Metric topology - Part 3
week-04
mod04lec23 - Closed Sets
mod04lec24 - Closure and Limit points
mod04lec25 - Continuous functions
mod04lec26 - Construction of continuous functions
mod04lec27 - Continuous functions on metric spaces - Part 1
mod04lec28 - Continuous functions on metric spaces - Part 2
week-05
mod05lec29 - Connectedness
mod05lec30 - Some conditions for Connectedness
mod05lec31 - Connectedness of the Real Line
mod05lec32 - Connectedness of a Linear Continuum
mod05lec33 - The Intermediate Value Theorem
week-06
mod06lec34 - Path-connectedness
mod06lec35 - Connectedness does not imply Path-connectedness - Part 1
mod06lec36 - Connectedness does not imply Path-connectedness - Part 2
mod06lec37 - Connected and Path-connected Components
mod06lec38 - Local connectedness and Local Path-connectedness
week-07
mod07lec39 - Compactness
mod07lec40 - Properties of compact spaces
mod07lec41 - The Heine-Borel Theorem
mod07lec42 - Tychonoff't theorem
mod07lec43 - Proof of Tychonoff's theorem - Part 1
mod07lec44 - Proof of Tychonoff's theorem - Part 2
week-08
mod08lec45 - Compactness in metric spaces
mod08lec46 - Lebesgue Number Lemma and the Uniform Continuity theorem
mod08lec47 - Different Kinds of Compactness
mod08lec48 - Equivalence of various compactness properties for Metric Spaces
mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces
week-09
mod09lec50 - Baire Spaces
mod09lec51 - Properties and Examples of Baire Spaces
mod09lec52 - The Baire Category Theorem
mod09lec53 - Complete Metric Spaces and the Baire Category theorem - Part 1
mod09lec54 - Complete Metric Spaces and the Baire Category theorem - Part 2
mod09lec55 - Application of the Baire Category theorem
week-10
mod10lec56 - Regular and Normal spaces
mod10lec57 - Properties and examples of regular and normal spaces
mod10lec58 - Urysohn's Lemma
mod10lec59 - Proof of Urysohn's Lemma
mod10lec60 - Tietze Extension theorem - Part 1
mod10lec61 - Tietze Extension theorem - Part 2
week-11
mod11lec62 - Compactness and Completeness in Metric spaces
mod11lec63 - The space of continuous functions - Part 1
mod11lec64 - The space of continuous functions - Part 2
mod11lec65 - Equicontinuity
mod11lec66 - Total boundedness and Equicontinuity - Part 1
mod11lec67 - Total boundedness and Equicontinuity - Part 2
week-12
mod12lec68 - Topology of compact convergence - Part 1
mod12lec69 - Topology of compact convergence - Part 2
mod12lec70 - Equicontinuity revisited - Part 1
mod12lec71 - Equicontinuity revisited - Part 2
mod12lec72 - Locally compact Hausdorff spaces
mod12lec73 - The Arzelà - Ascoli theorem
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Sl.No
Chapter Name
English
1
mod01lec01 - Introduction to Topology
PDF unavailable
2
mod01lec02 - Basic Set theory
PDF unavailable
3
mod01lec03 - Mathematical Logic - Part 1
PDF unavailable
4
mod01lec04 - Mathematical Logic - Part 2
PDF unavailable
5
mod01lec05 - Functions
PDF unavailable
6
mod01lec06 - Finite Sets - Part 1
PDF unavailable
7
mod01lec07 - Finite Sets - Part 2
PDF unavailable
8
mod01lec08 - Infinite Sets
PDF unavailable
9
mod01lec09 - Infinite Sets and Axiom of Choice
PDF unavailable
10
mod02lec10 - Definition of aTopology
PDF unavailable
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