Learn · An introduction to Point-Set-Topology Part - II
Lecture 4 of 60Week 1 : Chapter I - Introduction
Lecture 4 : Implicit and Inverse function theorems
Prof. Anant R Shastri · IIT Bombay
Credits and licence
- From
- An introduction to Point-Set-Topology Part - II, IIT Bombay (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lecture 1 : Preliminaries from Banach spaces
- Lecture 2 : Differentiation on Banach spaces
- Lecture 3 : Preliminaries from one-variable real analysis
- Lecture 4 : 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 : Alexandroff’s compactifiction
- Lecture 20 : Proper maps
- Lecture 21 : Stone-Cech compactification
- Lecture 22 : Stone-Weierstrass’ Theorems
- Lecture 23 : Real Stone-Weierstrass Theorem
- Lecture 24 : Complex and extended Stone-Weierstrass theorem
- Lecture 26 : Urysohn’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 Tychonoff’s theorem
- Lecture 34 : Wallman compactification
- Lecture 33 : Ultraclosed filters
- 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 exampels
- Lecture 41 : Dimensions of subspaces and Unions
- Lecture 42 : Sum theorem for higher dimensions
- Lecture 43 : Analytic Proof of Brouwer’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-cont.
- Lecture 61 : Surfaces
- Lecture 62 : Connected sum