SOFT π-OPEN SETS IN SOFT GENERALIZED TOPOLOGICAL SPACES

Authors : Jyothis Thomas, Sunil Jacob John

Pages : 53-66

View : 14 | Download : 10

Publication Date : 2015-06-01

Article Type : Research Paper

Abstract :The main purpose of this paper is to study some interesting properties of the soft mapping π : Sinsert ignore into journalissuearticles values(U);E → Sinsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values( ̃, 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