Non-Baire Proof Of Uniform Boundedness Theorem And Its Remarkable Applications

Abstract

In this paper our aim is to expound the importance of Non-Baire Proof of Uniform Boundedness theorem. We know that Baire’s Category Theorem is directly applied to prove Uniform Boundedness Theorem. We present here, a proof of the Uniform Boundedness Theorem that does not require the Baire’s Theorem in a similar fashion as proved by Alan D Sokal [1] but in a slightly different way.