Projective limits of paratopological vector spaces

Abstract

In this paper we describe various methods of constructing new paratopological vector spaces from given ones. First, we introduce the notion of a right dual of a paratopological vector space with the aim to define a right weak topology. We prove that, in a certain class of normed spaces, the classical weak topology is determined by a right weak topology. Next, the quotient topology in the context of paratopological vector spaces is discussed. Finally, we consider the projective limit of paratopological vector spaces and prove that every pseudoconvex space is a projective limit of quasi-normed spaces.