Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=58B5dEJReQ8&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=3 We finish introducing the basic notions of functional analysis including subspaces, quotient spaces, and seminorms (almost norms). Then we prove some necessary fundamental theorems for moving forward: the Baire Category Theorem and the Uniform Boundedness Theorem. The former theorem is the only category theory known to the instructor. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.