SOFT π-OPEN SETS IN SOFT GENERALIZED TOPOLOGICAL SPACES

Abstract

The main purpose of this paper is to study some interesting properties of the soft mapping π : S(U)E → S(U)E which satisfy the condition πFB ⊂ πFD whenever FB ⊂ FD ⊂ ̃. A new class of generalized soft open sets, called soft π-open sets is introduced and studied their basic properties. A soft set FG ⊂ ̃ is said to be a soft π-open set iff FG ⊂ πFG. The notions of soft interior and soft closure are generalized using these sets. We then introduce the concepts of soft π-interior iπFG, soft π-closure cπFG, soft π*FG of a soft set FG ⊂ ̃. Under suitable conditions on π, the soft π-interior iπFG and the soft π-closure cπFG of a soft set FG ⊂ ̃ are easily obtained by explicit formulas. The soft μ-semi-open sets, soft μ-pre-open sets, soft μ-α-open sets and soft μ-β-open sets for a given Soft Generalized Topological Space ( ̃, μ) can be obtained from soft π-open sets which are important for further research on soft generalized topology.

Keywords

• – Soft sets, soft generalized topology, soft mapping, soft π-open sets, soft π-interior, soft π-closure