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Afsan, Bin Mostakim Uzzal,Basu, Chanchal Kumar Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.1
Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-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 $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.
ON SOME NEW CLASSES OF COMPACT-LIKE BITOPOLOGICAL SPACES
B M Uzzal Afsan 충청수학회 2020 충청수학회지 Vol.33 No.2
In this paper, we have introduced a new type of covering property β t (ωr,s) -closedness, stronger than P t (ωr,s) -closedness [3] in terms of (r, s)-β-open sets [9] and β-ωt-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of β t (ωr,s) -closedness (namely, β t (ωr,s) -closedness modulo grill) and associated concepts have also been investigated.