Soft Separation Axioms in Soft Topological Spaces

Abstract

Shabir et. al [27] and D. N. Georgiou et. al [7], defined and studied some soft separation axioms, soft θ-continuity and soft connectedness in soft spaces using (ordinary) points of a topological space X. In this paper, we redefine and explore several properties of soft Ti, i = 0, 1, 2, soft regular, soft T3, soft normal and soft T4 axioms using soft points defined by I. Zorlutuna [30]. We also discuss some soft invariance properties namely soft topological property and soft hereditary property. We hope that these results will be useful for the future study on soft topology to carry out general framework for the practical applications and to solve the complicated problems containing uncertainties in economics, engineering, medical, environment and in general man-machine systems of various types.

On Two Classes of Soft Sets in Soft Topological Spaces

“…Then τ ( ) = a∈A a and by Theorem 8 Definition 17. [56] A STS (X, τ, A) is called soft T 1 if for any two soft points a x , a y ∈ SP(X, A) with x = y, there exist G, F ∈ τ such that a x ∈G − F and a y ∈F − G.…”

A Link between Topology and Soft Topology

“…Recently Muhammad Shabir and Munazza Naz introduced the notion of soft topology [10] and established that every soft topology induces a collection of topologies called the parametrized family of topologies induced by the soft topology. Several mathematicians published papers on applications of soft sets and soft topology [1,2,6,11,12,18]. Soft sets and soft topology have applications to data mining, image processing, decision making problems, spatial modeling and neural patterns [3,4,5,7,13.14,15,16,17].…”

On Soft Turning Points

“…In (4), Kharal and Ahmad gave the definition of mapping on soft classes and found some properties of image and inverse image of such mapping. Shabir and Ahmad (5), introduced separation axioms in the soft space that was defined by Zorlutuna. While the concept of soft ideal and likewise soft local function were first presented at (6,7).…”