Soft Homogeneous Components and Soft Products

Abstract

Firstly, for the topological spaces that contain a minimal open set, we obtain various inclusions between minimal open sets and homogeneity components. For a given soft topological space (X,τ,A), we define soft homogeneous components. We show that soft homogeneous components of (X,τ,A) form a soft partition of the absolute soft set. Also, we show that (X,τ,A) is soft homogeneous if and only if it has only one soft homogeneous component. Moreover, we study the relationships between the soft homogeneous components of (X,τ,A) and the homogeneous component. For the soft topological spaces that contain a minimal soft open set, we obtain various inclusions between minimal soft open sets and soft homogeneity components. In addition, we show that soft homeomorphisms stabilize soft homogeneous components. Additionally, we introduce two soft product theorems concerning soft homogeneity and soft minimality, respectively.

Keywords

• soft homogeneity
• soft minimality
• homogeneous components
• soft product