Pt(ω<sub>r,s)</sub>-CLOSED SPACES AND PRE-(ωr,s)t-θf-CLUSTER SETS

Abstract

Using (r, s)-preopen sets [14] and pre--closures [6], a new kind of covering property -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-(, s)t--cluster sets and (r, s)t--precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(, s)t--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 -closedness has also been established in terms of pre-(, s)t--cluster sets.