# An invitation to Topology

- Institution: IMSc
- Department: Mathematics
- Teacher: Prof. Indrava Roy
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106159)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106159)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [mod01lec01 - Introduction to Topology](https://invisiblenetwork.ai/learn/nptel/111106159/4dfc8dff7431) (Video)
2. [mod01lec02 - Basic Set theory](https://invisiblenetwork.ai/learn/nptel/111106159/5e72aa8b3b7a) (Video)
3. [mod01lec03 - Mathematical Logic - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/52ec93821e17) (Video)
4. [mod01lec04 - Mathematical Logic - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/8e15c8a6edd1) (Video)
5. [mod01lec05 - Functions](https://invisiblenetwork.ai/learn/nptel/111106159/bc5cc91b6ff0) (Video)
6. [mod01lec06 - Finite Sets - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/ab9e8d4ea2d8) (Video)
7. [mod01lec07 - Finite Sets - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/11094f6dd3b3) (Video)
8. [mod01lec08 - Infinite Sets](https://invisiblenetwork.ai/learn/nptel/111106159/85a33208e212) (Video)
9. [mod01lec09 - Infinite Sets and Axiom of Choice](https://invisiblenetwork.ai/learn/nptel/111106159/783aa600184e) (Video)
10. [mod02lec10 - Definition of aTopology](https://invisiblenetwork.ai/learn/nptel/111106159/b80d69d304b4) (Video)
11. [mod02lec11 - Examples of different topologies:](https://invisiblenetwork.ai/learn/nptel/111106159/ea8fa3ea9464) (Video)
12. [mod02lec12 - Basis for a topology](https://invisiblenetwork.ai/learn/nptel/111106159/da568f1ad57f) (Video)
13. [mod02lec13 - Various topologies on the real line](https://invisiblenetwork.ai/learn/nptel/111106159/c8b7edbb2f2c) (Video)
14. [mod02lec14 - Comparison of topologies - Part 1 : Finer and coarser topologies](https://invisiblenetwork.ai/learn/nptel/111106159/8a79a280dc01) (Video)
15. [mod02lec15 - Comparison of topologies - Part 2: Comparing the various topologies on R](https://invisiblenetwork.ai/learn/nptel/111106159/1048340aff2d) (Video)
16. [mod02lec16 - Basis and Sub-basis for a topology](https://invisiblenetwork.ai/learn/nptel/111106159/21ea4369c31f) (Video)
17. [mod03lec17 - Various topologies: the subspace topology](https://invisiblenetwork.ai/learn/nptel/111106159/2064a14e965c) (Video)
18. [mod02lec18 - The Product topology](https://invisiblenetwork.ai/learn/nptel/111106159/4d4e323a5658) (Video)
19. [mod02lec19 - Topologies on arbitrary Cartesian products](https://invisiblenetwork.ai/learn/nptel/111106159/ec1ef074e75b) (Video)
20. [mod02lec20 - Metric topology - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/476d7bf474ef) (Video)
21. [mod03lec21 - Metric topology - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/3df9f3a83601) (Video)
22. [mod03lec22 - Metric topology - Part 3](https://invisiblenetwork.ai/learn/nptel/111106159/a8f18bc8a790) (Video)
23. [mod04lec23 - Closed Sets](https://invisiblenetwork.ai/learn/nptel/111106159/b6829e794934) (Video)
24. [mod04lec24 - Closure and Limit points](https://invisiblenetwork.ai/learn/nptel/111106159/0ea9fb5ca25f) (Video)
25. [mod04lec25 - Continuous functions](https://invisiblenetwork.ai/learn/nptel/111106159/b24c4cb536b2) (Video)
26. [mod04lec26 - Construction of continuous functions](https://invisiblenetwork.ai/learn/nptel/111106159/4c08dba3f13c) (Video)
27. [mod04lec27 - Continuous functions on metric spaces - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/00e955763374) (Video)
28. [mod04lec28 - Continuous functions on metric spaces - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/3dc1982588e2) (Video)
29. [mod05lec29 - Connectedness](https://invisiblenetwork.ai/learn/nptel/111106159/4f3b67c04d5c) (Video)
30. [mod05lec30 - Some conditions for Connectedness](https://invisiblenetwork.ai/learn/nptel/111106159/231473e973cf) (Video)
31. [mod05lec31 - Connectedness of the Real Line](https://invisiblenetwork.ai/learn/nptel/111106159/48a2380a4c83) (Video)
32. [mod05lec32 - Connectedness of a Linear Continuum](https://invisiblenetwork.ai/learn/nptel/111106159/a07dbe018b27) (Video)
33. [mod05lec33 - The Intermediate Value Theorem](https://invisiblenetwork.ai/learn/nptel/111106159/24cc12aa387c) (Video)
34. [mod06lec34 - Path-connectedness](https://invisiblenetwork.ai/learn/nptel/111106159/f477563c9bdb) (Video)
35. [mod06lec35 - Connectedness does not imply Path-connectedness - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/7d8a32f8ba89) (Video)
36. [mod06lec36 - Connectedness does not imply Path-connectedness - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/30c3b63844a8) (Video)
37. [mod06lec37 - Connected and Path-connected Components](https://invisiblenetwork.ai/learn/nptel/111106159/e584b7057cbb) (Video)
38. [mod06lec38 - Local connectedness and Local Path-connectedness](https://invisiblenetwork.ai/learn/nptel/111106159/0a1341efdf10) (Video)
39. [mod07lec39 - Compactness](https://invisiblenetwork.ai/learn/nptel/111106159/84e2d1c33c34) (Video)
40. [mod07lec40 - Properties of compact spaces](https://invisiblenetwork.ai/learn/nptel/111106159/765fe466dbda) (Video)
41. [mod07lec41 - The Heine-Borel Theorem](https://invisiblenetwork.ai/learn/nptel/111106159/a2333f9286a3) (Video)
42. [mod07lec42 - Tychonoff't theorem](https://invisiblenetwork.ai/learn/nptel/111106159/5742062852ae) (Video)
43. [mod07lec43 - Proof of Tychonoff's theorem - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/913496e13a14) (Video)
44. [mod07lec44 - Proof of Tychonoff's theorem - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/886057649ab1) (Video)
45. [mod08lec45 - Compactness in metric spaces](https://invisiblenetwork.ai/learn/nptel/111106159/06e5f4e5cece) (Video)
46. [mod08lec46 - Lebesgue Number Lemma and the Uniform Continuity theorem](https://invisiblenetwork.ai/learn/nptel/111106159/ed50e42cc14b) (Video)
47. [mod08lec47 - Different Kinds of Compactness](https://invisiblenetwork.ai/learn/nptel/111106159/90552bc0deb3) (Video)
48. [mod08lec48 - Equivalence of various compactness properties for Metric Spaces](https://invisiblenetwork.ai/learn/nptel/111106159/8a89d874cd8a) (Video)
49. [mod08lec49 - Compactness and Sequential Compactness in arbitrary topological spaces](https://invisiblenetwork.ai/learn/nptel/111106159/b84281841f37) (Video)
50. [mod09lec50 - Baire Spaces](https://invisiblenetwork.ai/learn/nptel/111106159/5f0de607e798) (Video)
51. [mod09lec51 - Properties and Examples of Baire Spaces](https://invisiblenetwork.ai/learn/nptel/111106159/1f056a179306) (Video)
52. [mod09lec52 - The Baire Category Theorem](https://invisiblenetwork.ai/learn/nptel/111106159/4fd32cddb553) (Video)
53. [mod09lec53 - Complete Metric Spaces and the Baire Category theorem - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/820ce43c4c5f) (Video)
54. [mod09lec54 - Complete Metric Spaces and the Baire Category theorem - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/b23e90155bf8) (Video)
55. [mod09lec55 - Application of the Baire Category theorem](https://invisiblenetwork.ai/learn/nptel/111106159/56e13e6e2a4c) (Video)
56. [mod10lec56 - Regular and Normal spaces](https://invisiblenetwork.ai/learn/nptel/111106159/094763f62a5b) (Video)
57. [mod10lec57 - Properties and examples of regular and normal spaces](https://invisiblenetwork.ai/learn/nptel/111106159/50282305d53b) (Video)
58. [mod10lec58 - Urysohn's Lemma](https://invisiblenetwork.ai/learn/nptel/111106159/59ade8ed578d) (Video)
59. [mod10lec59 - Proof of Urysohn's Lemma](https://invisiblenetwork.ai/learn/nptel/111106159/145236e3bf75) (Video)
60. [mod10lec60 - Tietze Extension theorem - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/56f7117cf583) (Video)
61. [mod10lec61 - Tietze Extension theorem - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/12c750df8b57) (Video)
62. [mod11lec62 - Compactness and Completeness in Metric spaces](https://invisiblenetwork.ai/learn/nptel/111106159/61886f81cb92) (Video)
63. [mod11lec63 - The space of continuous functions - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/9dc8af498241) (Video)
64. [mod11lec64 - The space of continuous functions - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/d03f20214fae) (Video)
65. [mod11lec65 - Equicontinuity](https://invisiblenetwork.ai/learn/nptel/111106159/0cefb01b275a) (Video)
66. [mod11lec66 - Total boundedness and Equicontinuity - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/fba728a5e3af) (Video)
67. [mod11lec67 - Total boundedness and Equicontinuity - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/2938ec675b79) (Video)
68. [mod12lec68 - Topology of compact convergence - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/5da4d9b90c2f) (Video)
69. [mod12lec69 - Topology of compact convergence - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/72929ccde76a) (Video)
70. [mod12lec70 - Equicontinuity revisited - Part 1](https://invisiblenetwork.ai/learn/nptel/111106159/c67bf9268dff) (Video)
71. [mod12lec71 - Equicontinuity revisited - Part 2](https://invisiblenetwork.ai/learn/nptel/111106159/6390f4b0bb31) (Video)
72. [mod12lec72 - Locally compact Hausdorff spaces](https://invisiblenetwork.ai/learn/nptel/111106159/93a29e167f33) (Video)
73. [mod12lec73 - The Arzelà - Ascoli theorem](https://invisiblenetwork.ai/learn/nptel/111106159/a42bb5fdf102) (Video)
74. [Live Session 04-05-2022](https://invisiblenetwork.ai/learn/nptel/111106159/4dfc8dff7431-2) (Video)