On the Existence of Non-Zero Linear Continuous Functionals on Fréchet Spaces

Abstract

<p> This thesis is concerned with a necessary and sufficient condition for the existence of non-zero linear continuous functionals on Fréchet or more general topological vector spaces. The main idea is based on the famous Hahn-Banach theorem. Since the connection between Hahn-Banach theorem and separation theorems is well known, here we study some separation theorems as well.</p>