Bin Mostakim Uzzal Afsan and Chanchal Kumar Basu Sripat Singh College, West Bengal State University

Abstract : Using $(r,s)$-preopen sets [14] and pre-$\omega_t$-closures [6], a new kind of covering property $P_{(\omega_r,s)}^t$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-$(\omega_r,s)t$-$\theta_f$-cluster sets and $(r,s)t$-$\theta_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-$(\omega_r,s)t$-$\theta_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P_{(\omega_r,s)}^t$-closedness has also been established in terms of pre-$(\omega_r,s)t$-$\theta_f$-cluster sets.