Topological Vector Spaces
Lawrence Narici, Edward Beckenstein · 2010
Definition Topological Vector Space A topological vector space (TVS) is a vector space X over F = R or C endowed with a group topology that makes scalar multiplication a continuous map of F×X into X. In one sense we have arrived; in another, we have already been here since Chap. 2. We investigate topological vector spaces per se in this chapter, by which we mean that we examine the implications of the continuous scalar multiplication superimposed on the topological group structure.