An introduction to Point-Set-Topology Part-II JD5BG3SNGC

URI	`m2://res/JD5BG3SNGC`
Kind	course
Creators	Anant R Shastri (instructor)
Date	2022-07-08
Scope	in
Ids	course 02qyf5152:111101160

Expressions

e1: edition

Language	en
Date	2022-07-08

m1: page, IIT Bombay (record). nptel 111101160
m2: page, 2022-07-08 (record). nptel 111101160

Contents

part 1: Week 1 : Chapter I - Introduction
session 1: Lecture 1 : Preliminaries from Banach spaces
session 2: Lecture 2 : Differentiation on Banach spaces
session 3: Lecture 3 : Preliminaries from one-variable real analysis
session 4: Lecture 4 : Implicit and Inverse function theorems
session 5: Lecture 6 : Compact Hausdorff spaces
part 2: Week 2 : Chapter II - Compactness and Separation Axioms
session 6: Lecture 7 : Local compactness
session 7: Lecture 8 : Local Compactness-continued
session 8: Lecture 9 : The retraction functor k(X)
session 9: Lecture 10 : Compactly generated spaces
session 10: Lecture 11 : Paracompactness
part 3: Week 3 : Chapter III - Paracompactness and Partition of Unity
session 11: Lecture 12 : Partition of Unity
session 12: Lecture 13 : Paracompactness continued
session 13: Lecture 14 : Paracompactness continued.
session 14: Lecture 15 : Various Notions of Compactness
session 15: Lecture 16 : Total Boundedness
part 4: Week 4 : Chapter IV - Other Notions of Compactness
session 16: Lecture 17 : Arzel`a- Ascoli Theorem
session 17: Lecture 18 : Generalities on Compactification
session 18: Lecture 19 : Alexandroff’s compactifiction
session 19: Lecture 20 : Proper maps
session 20: Lecture 21 : Stone-Cech compactification
part 5: Week 5 : Chapter V - Compactifications
session 21: Lecture 22 : Stone-Weierstrass’ Theorems
session 22: Lecture 23 : Real Stone-Weierstrass Theorem
session 23: Lecture 24 : Complex and extended Stone-Weierstrass theorem
session 24: Lecture 26 : Urysohn’s Metrization theorem
part 6: Week 6 : Chapter VI - Metrization
session 25: Lecture 27 : Nagata Smyrnov Metrization theorem
session 26: Lecture 28 : Nets
session 27: Lecture 29 : Cofinal families subnets
session 28: Lecture 30 : Basics of Filters
session 29: Lecture 31 : Convergence Properties of Filters
part 7: Week 7 : Chapter VII - Nets and Filters
session 30: Lecture 32 : Ultrafilters and Tychonoff’s theorem
session 31: Lecture 34 : Wallman compactification
session 32: Lecture 33 : Ultraclosed filters
session 33: Lecture 35 : Wallman compactification-continued
session 34: Lecture 36 : Global Separation of Sets
part 8: Week 8 : Chapter VIII - Global Separation Axioms
session 35: Lecture 37 : More examples
session 36: Lecture 38 : Knaster-Kuratowski Example
session 37: Lecture 39 : Separation of Sets-continued
session 38: Lecture 40 : Definition of dimension and exampels
session 39: Lecture 41 : Dimensions of subspaces and Unions
part 9: Week 9 : Chapter IX - Wallman-Hurewicz Topological dimension theory
session 40: Lecture 42 : Sum theorem for higher dimensions
session 41: Lecture 43 : Analytic Proof of Brouwer’s Fixed Point Theorem
session 42: Lecture 44 : Local Separation to Global Separation
session 43: Lecture 45 : Partially Ordered sets
session 44: Lecture 46 : Principle of Transfinite Induction
part 10: Week 10 : Chapter X - Ordinals
session 45: Lecture 47 : Order topology
session 46: Lecture 48 : Ordinals
session 47: Lecture 49 : Ordinal Topology Continued
session 48: Lecture 50 : The Long Line
session 49: Lecture 51 : Motivation and definition
session 50: Lecture 52 : The exponential Correspondence
part 11: Week 11 : Chapter XI - Compact Open Topology
session 51: Lecture 53 : An Application to Quotient Maps
session 52: Lecture 54 : Groups of Homeomoprhisms
session 53: Lecture 55 : Definition and Exampels of Manifolds
session 54: Lecture 56 : Manifolds with Boundary
session 55: Lecture 57 : Homogeneity
part 12: Week 12 : Chapter XII - Manifolds
session 56: Lecture 58 : Homogeneity continued
session 57: Lecture 59 : Classification of 1-dim. manifolds
session 58: Lecture 60 : Classification of 1-dim. Manifolds-cont.
session 59: Lecture 61 : Surfaces
session 60: Lecture 62 : Connected sum

Catalogue records

nptel: 111101160 (manifestation)
nptel_video: 111101160 (manifestation)