Math400 - Functional Analysis - Exercises of Chapter 2 - Part 1

Exercise 1 is a simple application of the Hahn-Banach theorem in the plane. Exercise 3 explores some properties of the Minkowski functional of a convex set and establishes the following result. Given an open convex subset C of a normed space E, there is a homeomorphism from E to itself taking C into the open unit ball and taking the closure of C into the closed unit ball of E.