Principles: Uniform Boundedness

by | Aug 23, 2020 | Pure Maths

So last week we talked about the Baire Category Theorem, and this important tool will give us three equivalent theorems about the qualitative properties of operators on Banach spaces. Today we will begin with the first theorem, uniform boundedness. The proof of this...

Problem of the Week 1

by | Aug 16, 2020 | Problem Solving

So this problem is in line with the post of this week, Baire’s Lemma. Have a go and let me know your thoughts in the comments! Let be unbounded and open. Then let the set     Prove that is dense in...