Functional Analysis: Open Mapping Theorem -1

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!