On Irresolute Topological Vector Spaces

Abstract

In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector spaces is analog to the notion of topological vector spaces, but mathematically it behaves differently. An example is given to show that an irresolute topological vector space is not a topological vector space. It is proved that: 1) Irresolute topological vector spaces possess open hereditary property; 2) A homomorphism of irresolute topological vector spaces is irresolute if and only if it is irresolute at identity element; 3) In irresolute topological vector spaces, the scalar multiple of semi compact set is semi compact; 4) In irresolute topological vector spaces, every semi open set is translationally invariant.