An invitation to Topology D9MDS5SSBD

URI	`m2://res/D9MDS5SSBD`
Kind	course
Creators	Indrava Roy (instructor)
Date	2022-01-28
Scope	in

Expressions

e1: edition

Language	en
Date	2022-01-28

m1: page, IMSc (record). nptel 111106159
m2: page, 2022-01-28 (record). nptel 111106159

Contents

part 1: week-01
session 1: mod01lec01 - Introduction to Topology
session 2: mod01lec02 - Basic Set theory
session 3: mod01lec03 - Mathematical Logic - Part 1
session 4: mod01lec04 - Mathematical Logic - Part 2
session 5: mod01lec05 - Functions
session 6: mod01lec06 - Finite Sets - Part 1
session 7: mod01lec07 - Finite Sets - Part 2
session 8: mod01lec08 - Infinite Sets
session 9: mod01lec09 - Infinite Sets and Axiom of Choice
part 2: week-02
session 10: mod02lec10 - Definition of aTopology
session 11: mod02lec11 - Examples of different topologies:
session 12: mod02lec12 - Basis for a topology
session 13: mod02lec13 - Various topologies on the real line
session 14: mod02lec14 - Comparison of topologies - Part 1 : Finer and coarser topologies
session 15: mod02lec15 - Comparison of topologies - Part 2: Comparing the various topologies on R
session 16: mod02lec16 - Basis and Sub-basis for a topology
part 3: week-03
session 17: mod03lec17 - Various topologies: the subspace topology
session 18: mod02lec18 - The Product topology
session 19: mod02lec19 - Topologies on arbitrary Cartesian products
session 20: mod02lec20 - Metric topology - Part 1
session 21: mod03lec21 - Metric topology - Part 2
session 22: mod03lec22 - Metric topology - Part 3
part 4: week-04
session 23: mod04lec23 - Closed Sets
session 24: mod04lec24 - Closure and Limit points
session 25: mod04lec25 - Continuous functions
session 26: mod04lec26 - Construction of continuous functions
session 27: mod04lec27 - Continuous functions on metric spaces - Part 1
session 28: mod04lec28 - Continuous functions on metric spaces - Part 2
part 5: week-05
session 29: mod05lec29 - Connectedness
session 30: mod05lec30 - Some conditions for Connectedness
session 31: mod05lec31 - Connectedness of the Real Line
session 32: mod05lec32 - Connectedness of a Linear Continuum
session 33: mod05lec33 - The Intermediate Value Theorem
part 6: week-06
session 34: mod06lec34 - Path-connectedness
session 35: mod06lec35 - Connectedness does not imply Path-connectedness - Part 1
session 36: mod06lec36 - Connectedness does not imply Path-connectedness - Part 2
session 37: mod06lec37 - Connected and Path-connected Components
session 38: mod06lec38 - Local connectedness and Local Path-connectedness
part 7: week-07
session 39: mod07lec39 - Compactness
session 40: mod07lec40 - Properties of compact spaces
session 41: mod07lec41 - The Heine-Borel Theorem
session 42: mod07lec42 - Tychonoff't theorem
session 43: mod07lec43 - Proof of Tychonoff's theorem - Part 1
session 44: mod07lec44 - Proof of Tychonoff's theorem - Part 2
part 8: week-08
session 45: mod08lec45 - Compactness in metric spaces
session 46: mod08lec46 - Lebesgue Number Lemma and the Uniform Continuity theorem
session 47: mod08lec47 - Different Kinds of Compactness
session 48: mod08lec48 - Equivalence of various compactness properties for Metric Spaces
session 49: mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces
part 9: week-09
session 50: mod09lec50 - Baire Spaces
session 51: mod09lec51 - Properties and Examples of Baire Spaces
session 52: mod09lec52 - The Baire Category Theorem
session 53: mod09lec53 - Complete Metric Spaces and the Baire Category theorem - Part 1
session 54: mod09lec54 - Complete Metric Spaces and the Baire Category theorem - Part 2
session 55: mod09lec55 - Application of the Baire Category theorem
part 10: week-10
session 56: mod10lec56 - Regular and Normal spaces
session 57: mod10lec57 - Properties and examples of regular and normal spaces
session 58: mod10lec58 - Urysohn's Lemma
session 59: mod10lec59 - Proof of Urysohn's Lemma
session 60: mod10lec60 - Tietze Extension theorem - Part 1
session 61: mod10lec61 - Tietze Extension theorem - Part 2
part 11: week-11
session 62: mod11lec62 - Compactness and Completeness in Metric spaces
session 63: mod11lec63 - The space of continuous functions - Part 1
session 64: mod11lec64 - The space of continuous functions - Part 2
session 65: mod11lec65 - Equicontinuity
session 66: mod11lec66 - Total boundedness and Equicontinuity - Part 1
session 67: mod11lec67 - Total boundedness and Equicontinuity - Part 2
part 12: week-12
session 68: mod12lec68 - Topology of compact convergence - Part 1
session 69: mod12lec69 - Topology of compact convergence - Part 2
session 70: mod12lec70 - Equicontinuity revisited - Part 1
session 71: mod12lec71 - Equicontinuity revisited - Part 2
session 72: mod12lec72 - Locally compact Hausdorff spaces
session 73: mod12lec73 - The ArzelÃ - Ascoli theorem
part 13: Live Session
session 74: Live Session 04-05-2022

Catalogue records

nptel: 111106159 (manifestation)
nptel_video: 111106159 (manifestation)