Linear Topological Spaces

Abstract

In this thesis several topics from Topology, Linear Algebra, and Real Analysis are combined in the study of linear topological spaces. We begin with a brief look at linear spaces before moving on to study some basic properties of the structure of linear topological spaces including the localization of a topological basis. Then we turn our attention to linear spaces with a metric topology. In particular, we consider problems involving normed linear spaces, bounded linear transformations, and Hilbert spaces.