On separating axioms and similarity of soft topological spaces

Abstract

We will consider soft topologies defined on the same universe X with E as the set of parameters. It is shown that soft topologies are not equivalent to the general topologies defined on X . Moreover, some implications between soft separating axioms are different than those for ordinary topological spaces. The relation of similarity of soft topological spaces is also introduced and examined. The soft topologies T 1 and T 2 on X are called similar, if the families T 1 and T 2 are mutually coinitial. We study some basic properties of similar soft topological spaces: we check whether the family of all such spaces forms a lattice, we examine the relationship between similarity and being homeomorphic and consider the similarity of e-parameterized topologies.

On Two Classes of Soft Sets in Soft Topological Spaces

“…Lemma 1. [55] Let (X, τ, A) be a STS and let B be a soft base for τ. Then for every a ∈ A, the family {F (a) : F ∈ B} forms a base for the topology τ a on X.…”

On some generated soft topological spaces and soft homogeneity

“… [16] For any topological space true(X,ℑtrue) and any set of parameters A, true(X,τ(ℑ),Atrue) is a STS.…”

“… [16] If true(X,ℑtrue) is a topological space and A is any set of parameters, then true(τ(ℑ)true)agoodbreakafter=ℑ for all a∈A .…”

“…The notion of soft topological spaces was introduced in [10]. Then, Mathematicians modified several concepts of classical topological spaces to include soft topological spaces (see [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]). A topological space true(X,ℑtrue) is homogeneous if for all x,y∈X, there is a homeomorphism f:(X,ℑ)false⟶(X,ℑ) such that ffalse(xfalse)goodbreakafter=y.…”

“…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.…”