On Two Classes of Soft Sets in Soft Topological Spaces

Abstract

In this paper, we define soft ω-open sets and strongly soft ω-open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω-open sets in soft topological spaces. Also, we study the relationships between the ω-open sets of a given indexed family of topological spaces and the soft ω-open sets (resp. strongly soft ω-open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω-open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

Soft ω*-Paracompactness in Soft Topological Spaces

“…Throughout this paper, we use the notions and terminology in [1] and [2]; moreover, TS and STS stand for "topological space" and "soft topological space," respectively. Recently, classical methods have been applied to several problems in various fields, such as engineering, social sciences, and medical sciences.…”

“…For an STS (X, τ, A), the members of τ are called soft open sets, and their soft complements are called soft closed sets. Several topological concepts have been extended to the context of STSs [1,2,. The concept of ω-open set was introduced in [29] as a weaker form of an open set as follows: Let (X, ) be a TS and let U ⊆ X; then, U is called ω-open if for every x ∈ U , there is an open set V and a countable subset C ⊆ X such that x ∈ V − C ⊆ U .…”

“…Using ω-open sets, the concept of ω * -paracompactness was defined and studied in ordinary TSs [36]. In [2], the concept of ω-openness was extended to include STSs as follows: Let (X, τ, A) be an STS, and let G ∈ SS(X, A); then, G is called a soft ω-open set if for all a x ∈ H, there exist F ∈ τ and H ∈ CSS(X, A) such that a x ∈F − H ⊆G. The collection of all soft ω-open sets in (X, τ, A) is denoted by τ ω .…”

“…The collection of all soft ω-open sets in (X, τ, A) is denoted by τ ω . It was proved in [2] that (X, τ ω , A) is an STS with τ ⊆ τ ω .…”

A new class between theta open sets and theta omega open sets

“…Area of research related to ω -open sets was and still is hot, authors in [9] , [10] , [11] , [12] , [13] , [14] , [15] have obtained several interesting results related to these sets. Authors in [16] , [17] , [18] introduced ω -open sets in fuzzy topological spaces and soft ts's. Recently by means of open sets and ω -open sets, authors in [19] introduced the notion of -open sets as a class between open sets and θ -open sets, then authors in [20] , [21] continued the study of [19] .…”