NOC:An Introduction to Point-Set-Topology - Part II

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Anant R Shastri

NPTEL Co-ordinating Institute : IIT Bombay

NPTEL Lecture Count : 62

NPTEL Course Size : 6.5 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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