# Essentials of Topology

- Institution: IIT-ISM Dhanbad
- Department: Mathematics
- Teacher: Prof. S. P. Tiwari
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105169)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105169)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 1 : Introduction](https://invisiblenetwork.ai/learn/nptel/111105169/16c7551ed409) (YouTube)
2. [Lecture 2 : Sets and Functions-I](https://invisiblenetwork.ai/learn/nptel/111105169/8c7fe7017fb4) (YouTube)
3. [Lecture 3 : Sets and Functions-I](https://invisiblenetwork.ai/learn/nptel/111105169/9b6153c80732) (YouTube)
4. [Lecture 4: Sets and Functions-III](https://invisiblenetwork.ai/learn/nptel/111105169/7decf902d142) (YouTube)
5. [Lecture 5 : Sets and Functions-IV](https://invisiblenetwork.ai/learn/nptel/111105169/218cc1499930) (YouTube)
6. [Lecture 6 : Metric Spaces](https://invisiblenetwork.ai/learn/nptel/111105169/4838293f383a) (YouTube)
7. [Lecture 7 : Topological Spaces](https://invisiblenetwork.ai/learn/nptel/111105169/3751b84861f0) (YouTube)
8. [Lecture 8 : Topological Spaces (Examples)](https://invisiblenetwork.ai/learn/nptel/111105169/80d55a4a8524) (YouTube)
9. [Lecture 9 : Topologies on R-I](https://invisiblenetwork.ai/learn/nptel/111105169/6f73647eca68) (YouTube)
10. [Lecture 10 : Topologies on R-II](https://invisiblenetwork.ai/learn/nptel/111105169/1e5b165eae2e) (YouTube)
11. [Lecture 11 : Comparison of topologies](https://invisiblenetwork.ai/learn/nptel/111105169/2f1934118194) (YouTube)
12. [Lecture 12 : Closed sets](https://invisiblenetwork.ai/learn/nptel/111105169/d938e7796cca) (YouTube)
13. [Lecture 13 : Basis for a topology-I](https://invisiblenetwork.ai/learn/nptel/111105169/6856cdecadac) (YouTube)
14. [Lecture 14 : Basis for a topology-II](https://invisiblenetwork.ai/learn/nptel/111105169/a0912c6bb254) (YouTube)
15. [Lecture 15 : A topology on R^2](https://invisiblenetwork.ai/learn/nptel/111105169/98d2fbd1a833) (YouTube)
16. [Lecture 16 : Subbasis and Neighborhood](https://invisiblenetwork.ai/learn/nptel/111105169/9faa0261ddca) (YouTube)
17. [Lecture 17 : Limit points of sets](https://invisiblenetwork.ai/learn/nptel/111105169/1cfce720e651) (YouTube)
18. [Lecture 18 : Closure of sets](https://invisiblenetwork.ai/learn/nptel/111105169/528f62034031) (YouTube)
19. [Lecture 19 : Interior and boundary of sets](https://invisiblenetwork.ai/learn/nptel/111105169/58cf690ea396) (YouTube)
20. [Lecture 20 : Subspaces](https://invisiblenetwork.ai/learn/nptel/111105169/054061658638) (YouTube)
21. [Lecture 21 : Product topology](https://invisiblenetwork.ai/learn/nptel/111105169/3e1ccdb7a244) (YouTube)
22. [Lecture 22 : Product and Box topologies](https://invisiblenetwork.ai/learn/nptel/111105169/0aaeecd2fe37) (YouTube)
23. [Lecture 23 : The Quotient topology](https://invisiblenetwork.ai/learn/nptel/111105169/42964cdffd34) (YouTube)
24. [Lecture 24 : Krakowski closure/interior operator](https://invisiblenetwork.ai/learn/nptel/111105169/df3ae5deb28a) (YouTube)
25. [Lecture 25 : Countability axioms-I](https://invisiblenetwork.ai/learn/nptel/111105169/233974cdba04) (YouTube)
26. [Lecture 26 : Countability axioms-II](https://invisiblenetwork.ai/learn/nptel/111105169/81970858b310) (YouTube)
27. [Lecture 27 : Countability axioms-III](https://invisiblenetwork.ai/learn/nptel/111105169/88c6604c98c2) (YouTube)
28. [Lecture 28 : Continuous functions-I](https://invisiblenetwork.ai/learn/nptel/111105169/ff15077c5330) (YouTube)
29. [Lecture 29 : Continuous functions-II](https://invisiblenetwork.ai/learn/nptel/111105169/ea7a22bb4e6b) (YouTube)
30. [Lecture 30 : Continuous functions-III](https://invisiblenetwork.ai/learn/nptel/111105169/f153131aae74) (YouTube)
31. [Lecture 31 : Continuous functions-IV](https://invisiblenetwork.ai/learn/nptel/111105169/02561004cf62) (YouTube)
32. [Lecture 32 : Homeomorphisms-I](https://invisiblenetwork.ai/learn/nptel/111105169/e39a8709a8e4) (YouTube)
33. [Lecture 33 : Homeomorphisms-II](https://invisiblenetwork.ai/learn/nptel/111105169/ebf9a9be1ee9) (YouTube)
34. [Lecture 34 : Homeomorphisms-III](https://invisiblenetwork.ai/learn/nptel/111105169/4852a48cc248) (YouTube)
35. [Lecture 35 : Connectedness-I](https://invisiblenetwork.ai/learn/nptel/111105169/91a4aa014298) (YouTube)
36. [Lecture 36 : Connectedness-II](https://invisiblenetwork.ai/learn/nptel/111105169/21374be294c5) (YouTube)
37. [Lecture 37 : Connectedness-III](https://invisiblenetwork.ai/learn/nptel/111105169/7feb53e18a36) (YouTube)
38. [Lecture 38 : Connectedness-IV](https://invisiblenetwork.ai/learn/nptel/111105169/45008b90161a) (YouTube)
39. [Lecture 39 : Connectedness-V](https://invisiblenetwork.ai/learn/nptel/111105169/3622f57fb6a3) (YouTube)
40. [Lecture 40 : Connectedness-VI](https://invisiblenetwork.ai/learn/nptel/111105169/de9ed6f595c1) (YouTube)
41. [Lecture 41 : Connectedness-VII](https://invisiblenetwork.ai/learn/nptel/111105169/a7d139422881) (YouTube)
42. [Lecture 42 : Connectedness-VIII](https://invisiblenetwork.ai/learn/nptel/111105169/5fc962ccf0d6) (YouTube)
43. [Lecture 43 : Path connectedness-I](https://invisiblenetwork.ai/learn/nptel/111105169/28e1f3d94c7a) (YouTube)
44. [Lecture 44 : Path connectedness-III](https://invisiblenetwork.ai/learn/nptel/111105169/b9d0ab139df7) (YouTube)
45. [Lecture 45 : Path connectedness-III](https://invisiblenetwork.ai/learn/nptel/111105169/26e4b50f1326) (YouTube)
46. [Lecture 46 : Path components and Local connectedness](https://invisiblenetwork.ai/learn/nptel/111105169/b220de57f440) (YouTube)
47. [Lecture 47 : Local connectedness](https://invisiblenetwork.ai/learn/nptel/111105169/84c91f4d6cb9) (YouTube)
48. [Lecture 48 : Local path connectedness](https://invisiblenetwork.ai/learn/nptel/111105169/5af56c68edc6) (YouTube)
49. [Lecture 49 : Compactness-I](https://invisiblenetwork.ai/learn/nptel/111105169/3cca34544b69) (YouTube)
50. [Lecture 50 : Compactness-II](https://invisiblenetwork.ai/learn/nptel/111105169/307b60b9aa92) (YouTube)
51. [Lecture 51 : Compactness-III](https://invisiblenetwork.ai/learn/nptel/111105169/8ab38e45def2) (YouTube)
52. [Lecture 52 : Compactness-IV](https://invisiblenetwork.ai/learn/nptel/111105169/e5b16426460f) (YouTube)
53. [Lecture 53 : Compactness-V](https://invisiblenetwork.ai/learn/nptel/111105169/3e6572e9a8e1) (YouTube)
54. [Lecture 54 : Compactness-VI](https://invisiblenetwork.ai/learn/nptel/111105169/f7ec11ddf827) (YouTube)
55. [Lecture 55 : Compactness-VII](https://invisiblenetwork.ai/learn/nptel/111105169/dd558ac02f7b) (YouTube)
56. [Lecture 56 : Compactness-VIII](https://invisiblenetwork.ai/learn/nptel/111105169/1bbfb88bf3f8) (YouTube)
57. [Lecture 57 : Compactness-IX](https://invisiblenetwork.ai/learn/nptel/111105169/f218b53a52c9) (YouTube)
58. [Lecture 58 : Compactness-X](https://invisiblenetwork.ai/learn/nptel/111105169/9d2f01b1a40d) (YouTube)
59. [Lecture 59 : One-point compactifications-I](https://invisiblenetwork.ai/learn/nptel/111105169/9eded3a5c727) (YouTube)
60. [Lecture 60 : One-point compactifications-II](https://invisiblenetwork.ai/learn/nptel/111105169/5887e2ee597c) (YouTube)
61. [Lecture 61 : Separation axioms-I](https://invisiblenetwork.ai/learn/nptel/111105169/151303acb43a) (YouTube)
62. [Lecture 62 : Separation axioms-II](https://invisiblenetwork.ai/learn/nptel/111105169/6668a481aaf3) (YouTube)
63. [Lecture 63 : Separation axioms-III](https://invisiblenetwork.ai/learn/nptel/111105169/758005b2da9d) (YouTube)
64. [Lecture 64 : Separation axioms-IV](https://invisiblenetwork.ai/learn/nptel/111105169/64a168bac4d7) (YouTube)
65. [Lecture 65 : Separation axioms-V](https://invisiblenetwork.ai/learn/nptel/111105169/daa909dbcee6) (YouTube)
66. [Lecture 66 : Separation axioms-VI](https://invisiblenetwork.ai/learn/nptel/111105169/f399461dff1e) (YouTube)
67. [Lecture 67 :Separation axioms-VII](https://invisiblenetwork.ai/learn/nptel/111105169/d336fa3c991f) (YouTube)
68. [Lecture 68 : Separation axioms-VIII](https://invisiblenetwork.ai/learn/nptel/111105169/756a56b53dd2) (YouTube)
69. [Lecture 69 : Tychonoff theorem-I](https://invisiblenetwork.ai/learn/nptel/111105169/a356f9639140) (YouTube)
70. [Lecture 70 : Tychonoff theorem-II](https://invisiblenetwork.ai/learn/nptel/111105169/ca625e178676) (YouTube)
71. [Lecture 71 : Stone-Cech compactification-I](https://invisiblenetwork.ai/learn/nptel/111105169/b008c132f5f9) (YouTube)
72. [Lecture 72 : Stone-Cech compactification-II](https://invisiblenetwork.ai/learn/nptel/111105169/fb213c1b5a92) (YouTube)