On some generated soft topological spaces and soft homogeneity

Abstract

We introduce soft homogeneity as an extension of homogeneity in ordinary topological spaces. Based on the generated soft topology of a given indexed family of classical topologies inspite of a one topology given by Terepeta in [16] , we investigate soft minimal open set and homogeneity relation between the generated soft topology and the given indexed family of topologies. We introduce several results, examples and counterexamples.

On Two Classes of Soft Sets in Soft Topological Spaces

“…Definition 6. [21] Let X be an initial universe and let A be a set of parameters. For any a ∈ A and Y ⊆ X, the soft set F ∈ SS(X, A) defined by…”

“…Proposition 8. [21] Let X be an initial universe and let A be a set of parameters. Let { a : a ∈ A} be an indexed family of topologies on X.…”

“…The notion of soft topological spaces is introduced in [6]. Then researchers modified several concepts of classical topological spaces to include soft topological spaces, some recently published soft topological papers are appeared in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For the purpose of improving some known topological theorems, Hdeib [27] introduced the notion of ω-closed sets as a weaker notion of closed sets as follows: Let (X, ) be a topological space and A a subset of X.…”

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 .…”