A new approach to vague soft toplogical structures concerning soft points

Abstract

This paper concerns the study of the notion of vague soft beta-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms beta(i) (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of beta(i) (with i =, 1, 2, 3, 4) spaces with the closer of vague soft beta-open set by means of soft points, vague soft countable spaces and their relationship with beta(i) (with i =, 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.