Casey Rodriguez: Introduction to Functional Analysis, III. Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem

The previous lecture in this series is here. The next lecture in this series is here.

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.

These videos are of a lecture course by Casey Rodriguez at the Massachusetts Institute of Technology in 2021, and made available as part of its OpenCourseWare initiative.