Some Results Over Thin-Thick Sets in Cone Locally Convex Spaces

Abstract

In this article, it is investigated some concepts of normed space like norming, thin-thick sets in cone locally convex spaces. It is also worked some impacts of thick sets over the uniform quasi-boundedness principles in cone locally convex spaces such that weak*-bounded sets are strong*-bounded iff the space is a B - M space. It is demonstrated that these principles emerge under some weaker conditions with aim to thick sets. Moreover, it is displayed that the concept of thick is a duality invariant, that is, all suitable topologies for some cone locally convex space have the same thick sets.