Linear Topological Spaces

Abstract

This chapter is largely preliminary in nature; it consists of a brief review of some of the terminology and the elementary theorems of general topology, an examination of the new concept “linear topological space” in terms of more familiar notions, and a comparison of this new concept with the mathematical objects of which it is an abstraction. After an introductory section on topology, we consider linear topological spaces, subspaces, quotient spaces, product spaces, and linear functions. With the exception of a few simple propositions relating to circled sets, these theorems are specializations of familiar results on topological groups (in other words, little use is made of scalar multiplication).