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Functional Analysis: Open Mapping Theorem -1
Автор: S Kumaresan
Загружено: 2023-01-04
Просмотров: 1448
Описание:
This is the first session of a two part series on the open mapping theorem.
Timestamp provided by Joson Josh Martires Henriques.
00:00 Disclaimer
02:11 Statement of Open Mapping Theorem
03:14 What are open maps?
05:15 Equivalent condition to check openness of a map between metric spaces/normed linear spaces
19:31 An important observation!
21:15 Strategy of the proof
22:49 Geometric ideas - Image of unit ball is convex and symmetric
29:27 Recall Baire's theorem and using it in the current proof
33:21 Closure of unit ball is convex and symmetric
40:50 Concluding the proof that 0 is an interior point of the closure of T(B_x)
44:44 A separate lemma!
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