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Course11110516972 lectures

Essentials of Topology

Prof. S. P. Tiwari · IIT-ISM Dhanbad

Start with lecture 1 At NPTEL

About

This course aims to explore the foundations of mathematics at a level and at depth for someone ambitious to study higher mathematics. This course begins with the basic concepts of sets, functions, and metric spaces, need for the study of topology. Further, topology is discussed from fundamental to higher levels, which are essentials for a topology learner.

Intended audience: Under graduate

Prerequisites: One course in real analysis available on NPTEL Portal is desirable.

Lectures

Week 1

  1. Lecture 1 : Introduction YouTube
  2. Lecture 2 : Sets and Functions-I YouTube
  3. Lecture 3 : Sets and Functions-I YouTube
  4. Lecture 4: Sets and Functions-III YouTube
  5. Lecture 5 : Sets and Functions-IV YouTube
  6. Lecture 6 : Metric Spaces YouTube
  7. Lecture 7 : Topological Spaces YouTube

Week 2

  1. Lecture 8 : Topological Spaces (Examples) YouTube
  2. Lecture 9 : Topologies on R-I YouTube
  3. Lecture 10 : Topologies on R-II YouTube
  4. Lecture 11 : Comparison of topologies YouTube
  5. Lecture 12 : Closed sets YouTube
  6. Lecture 13 : Basis for a topology-I YouTube

Week 3

  1. Lecture 14 : Basis for a topology-II YouTube
  2. Lecture 15 : A topology on R^2 YouTube
  3. Lecture 16 : Subbasis and Neighborhood YouTube
  4. Lecture 17 : Limit points of sets YouTube
  5. Lecture 18 : Closure of sets YouTube
  6. Lecture 19 : Interior and boundary of sets YouTube

Week 4

  1. Lecture 20 : Subspaces YouTube
  2. Lecture 21 : Product topology YouTube
  3. Lecture 22 : Product and Box topologies YouTube
  4. Lecture 23 : The Quotient topology YouTube
  5. Lecture 24 : Krakowski closure/interior operator YouTube

Week 5

  1. Lecture 25 : Countability axioms-I YouTube
  2. Lecture 26 : Countability axioms-II YouTube
  3. Lecture 27 : Countability axioms-III YouTube
  4. Lecture 28 : Continuous functions-I YouTube
  5. Lecture 29 : Continuous functions-II YouTube
  6. Lecture 30 : Continuous functions-III YouTube

Week 6

  1. Lecture 31 : Continuous functions-IV YouTube
  2. Lecture 32 : Homeomorphisms-I YouTube
  3. Lecture 33 : Homeomorphisms-II YouTube
  4. Lecture 34 : Homeomorphisms-III YouTube
  5. Lecture 35 : Connectedness-I YouTube

Week 7

  1. Lecture 36 : Connectedness-II YouTube
  2. Lecture 37 : Connectedness-III YouTube
  3. Lecture 38 : Connectedness-IV YouTube
  4. Lecture 39 : Connectedness-V YouTube
  5. Lecture 40 : Connectedness-VI YouTube
  6. Lecture 41 : Connectedness-VII YouTube
  7. Lecture 42 : Connectedness-VIII YouTube

Week 8

  1. Lecture 43 : Path connectedness-I YouTube
  2. Lecture 44 : Path connectedness-III YouTube
  3. Lecture 45 : Path connectedness-III YouTube
  4. Lecture 46 : Path components and Local connectedness YouTube
  5. Lecture 47 : Local connectedness YouTube
  6. Lecture 48 : Local path connectedness YouTube

Week 9

  1. Lecture 49 : Compactness-I YouTube
  2. Lecture 50 : Compactness-II YouTube
  3. Lecture 51 : Compactness-III YouTube
  4. Lecture 52 : Compactness-IV YouTube
  5. Lecture 53 : Compactness-V YouTube
  6. Lecture 54 : Compactness-VI YouTube

Week 10

  1. Lecture 55 : Compactness-VII YouTube
  2. Lecture 56 : Compactness-VIII YouTube
  3. Lecture 57 : Compactness-IX YouTube
  4. Lecture 58 : Compactness-X YouTube
  5. Lecture 59 : One-point compactifications-I YouTube
  6. Lecture 60 : One-point compactifications-II YouTube

Week 11

  1. Lecture 61 : Separation axioms-I YouTube
  2. Lecture 62 : Separation axioms-II YouTube
  3. Lecture 63 : Separation axioms-III YouTube
  4. Lecture 64 : Separation axioms-IV YouTube
  5. Lecture 65 : Separation axioms-V YouTube
  6. Lecture 66 : Separation axioms-VI YouTube

Week 12

  1. Lecture 67 :Separation axioms-VII YouTube
  2. Lecture 68 : Separation axioms-VIII YouTube
  3. Lecture 69 : Tychonoff theorem-I YouTube
  4. Lecture 70 : Tychonoff theorem-II YouTube
  5. Lecture 71 : Stone-Cech compactification-I YouTube
  6. Lecture 72 : Stone-Cech compactification-II YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT-ISM Dhanbad
Department
Mathematics
Teacher
Prof. S. P. Tiwari
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Kharagpur.
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