On Pretopological Vector Spaces

Abstract

The purpose of the present paper is to introduce the new class of topological spaces, namely pretopological vector spaces. We study some of the basic properties of pretopological vector spaces and investigate their relationships with certain existing spaces. Along with other results, it is proved that translation of an open (resp. closed) set in a pretopological vector space is pre-open (resp. pre-closed), that translations and dilations  on pretopological vector spaces are precontinuous.