On near open sets in bitopological spaces

Abstract

In this paper we introduced two new classes of sets in bitopological spaces, the first type is weaker than \(ij\)-\(\Omega\)-closed sets namely, \(ij\)-\(\Omega^{^{*}}\)-closed sets, and the second type called \(ij\)-\(\Omega^{^{**}}\)-closed sets which lies between the class of \(ij\)-\(\Omega\)-closed sets and the class of \(ij\)-\(g\)-closed sets. We find some basic properties and applications of these sets. We also, introduce new bitopological separation axioms and new type of continuous functions between bitopological spaces. Finally, we prove that some of the introduced bitopological separation properties are preserved under some types of continuous functions.