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【拓扑与分析】Topology & Analysis (James Cook)

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2019-09-27 20:45:13

https://www.youtube.com/playlist?list=PLBY4G2o7DhF2vH4ZluTCWRTAgmCefB_pE 教材是 Jänich 的《Topology》（世界图书出过影印版）、Greene & Gamelin《Introduction to Topology》。

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Lecture 01 metric spaces, 1-18-19, part 1

59:51

Lecture 02 metric spaces, 1-18-19, part 2

33:45

Lecture 03 compactness in metric space, 1-21-19 part 1

59:51

Lecture 04 compactness in metric space, 1-21-19 part 2

32:12

Lecture 05 continuity and normed linear spaces, 1-27-19 part 1

42:49

Lecture 06 contraction mapping technique, 1-27-19 part 2

32:26

Lecture 07 definition of topology, open, closed, nbhd, 1-28-19 part 1

59:51

Lecture 08 definition of topology, open, closed, nbhd, 1-28-19 part 2

17:04

Lecture 09 basis and weird topologies, 2-1-19 part 1

59:51

Lecture 10 basis and weird topologies, 2-1-19 part 2

27:51

Lecture 11 from Hausdorff to Compactness, 2-4-19 part 1

59:51

Lecture 12 from Hausdorff to Compactness, 2-4-19 part 2

35:57

Lecture 13 connected and path connected, 2-8-19 part 1

59:51

Lecture 14 connected and path connected, 2-8-19 part 2

16:12

Lecture 15 functions, pasting lemma, Zariski Top, 2-11-19 part 1

59:51

Lecture 16 functions, pasting lemma, Zariski Top, 2-11-19 part 2

15:15

Lecture 17 axiom of choice, every vector space has basis, 2-15-19 part 1

59:51

Lecture 18 basis, word on compact products, 2-15-19 part 2

21:56

Lecture 19 products and quotients, 2-18-19 part 1

59:51

Lecture 20 building quotients, 2-18-19 part 2

05:07

Lecture 21 quotient spaces again, 2-22-19 part 1

59:51

Lecture 22 topological group discussion, 2-22-19 part 2

12:15

Lecture 23 homogeneous spaces, 2-25-19 part 1

59:51

Lecture 24 homogeneous spaces, 2-25-19 part 2

23:58

Lecture 25 homotopy and fundamental group, 3-1-19 part 1

51:20

Lecture 26 homotopy and fundamental group, 3-1-19 part 2

24:57

Lecture 27 fundamental group, 3-4-19 part 1

59:51

Lecture 28 induced homomorphism - 3-4-19 part 2

24:02

Lecture 29 Simplicial Homology in a day, 3-8-19 part 1

59:51

Lecture 30 Simplicial Homology in a day, 3-8-19 part 2

29:05

Lecture 31 covering maps and lifts, 3-18-19 part 1

59:51

Lecture 32 covering maps, and lifts,3-18-19 part 2

27:50

Lecture 33 path lifts and fundamental group, 3-22-19 part 1

59:51

Lecture 34 path lifts and fundamental group, 3-22-19 part 2

13:35

Lecture 35 winding number, big fixed point theorems, 3-25-19 part 1

59:51

Lecture 36 winding number, big fixed point theorems, 3-25-19 part 2

31:40

Lecture 37 a word on categories, 3-29-19 part 1

59:51

Lecture 38 a word on categories, 3-29-19 part 2

03:07

Lecture 39 exterior measure leading to Lesbegue, 4-1-19 part 1

59:51

Lecture 40 exterior measure leading to Lesbegue, 4-1-19 part 2

21:55

Lecture 41 measurable functions, 4-5-19 part 1

59:51

Lecture 42 measurable functions, 4-5-19 part 2

25:32

Lecture 43 simple functions and Lebesgue integral, 4-12-19 part 1

59:51

Lecture 44 simple functions and Lebesgue integral, 4-12-19 part 2

15:53

Lecture 45 Lebesgue integral Stage 2, 4-15-19, part 1

59:51

Lecture 46 Lebesgue integral Stage 2, 4-15-19, part 2

24:27

Lecture 47 Lebesgue Stage 3 and 4, 4-19-19 part 1

59:51

Lecture 48 Lebesgue Stage 3 and 4, 4-19-19 part 2

30:22

Lecture 49 dominated convergence theorem and more, 4-26-19 part 1

59:51

Lecture 50 dominated convergence theorem and more, 4-26-19 part 2

32:32

Lecture 51 a brief intro to Hilbert Space, 4-29-19 part 1

59:51

Lecture 52 an invitation to learn what I don't yet know, 4-29-19 part 2

24:52

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