Some operators of a soft set and soft connected spaces using soft somewhere dense sets

Abstract

In the current work, we continue studying new notions and properties of soft somewhere dense and soft cs-dense sets. We introduce the concepts of S-interior, S-closure, S-boundary and S-limit points of a soft set and give some explicit formulas to calculate them. Also, we investigate their main features and show the relationships among them with the aid of counterexamples. Moreover, we prove that the operators of S-interior and S-closure are preserved under the finite soft product space. Finally, we formulate a new type of soft connectedness and study main properties in details. In general, we conclude some interrelations of these concepts which are kept between soft topology and its parametric topologies and explain the important role of extended soft topological and soft hyperconnected spaces regarding this point.

Subject Classification: (2010):

• 54A05
• 54B10
• 03E72

Keywords:

• Somewhere dense set
• Extended soft topology
• S-interior point
• S-closure point
• S-boundary point
• S-limit point
• Soft product spaces
• S-soft connected space