A New Analytic Study of Fundamental Filter in Topological Vector Space via Di-Proximit Structure

Abstract

    This article introduces the concept of Di- proximit space and examines several results in this new context. We provide new definitions of the terms Di-proximit space, Di-proximit  topological vector space, found relation between tower and Di-proximit. We provide new definitions of the terms cluster point in Di- proximit topological vector space , Di – Cauchy filter ,Di-convergent filter  in Di-proximit topological vector space and the relationship between Di – Cauchy filter and Di-convergent filter in Di-proximit topological vector space.