Soft connectivity and soft θ-connectivity relative to a soft topological space

Abstract

Let (Y, σ, B) be a soft topological space. We introduce two new classes of soft subsets of (Y, σ, B): soft connectedness relative to (Y, σ, B) and soft θ-connectedness relative to (Y, σ, B). We show that the class of soft connected subsets relative to (Y, σ, B) includes the class of soft θ-connected subsets relative to (Y, σ, B), but that these two classes do not always coincide. However, they coincide when (Y, σ, B) is soft regular. We have provided several properties for each of these classes of soft sets. As two main results, we prove that for a given soft function fpu : (Y, σ, B) ⟶ (Y, σ, B) and a soft subset H of (Y, σ, B), the soft set fpu (H) is θ-connected relative to (Y, σ, B) if (fpu is soft weakly continuous and H is connected relative to (Y, σ, B)) or (fpu is soft θ-continuous and H is θ-connected relative to (Y, σ, B)). Also, we investigate the correspondence between our new concepts in a soft topological space and their corresponding topological spaces properties. Moreover, we provide some examples to illustrate the obtained results and relationships.