Ptr,s)-CLOSED SPACES AND PRE-(ωr,s)t-θf-CLUSTER SETS

Title & Authors
Ptr,s)-CLOSED SPACES AND PRE-(ωr,s)t-θf-CLUSTER SETS
Afsan, Bin Mostakim Uzzal; Basu, Chanchal Kumar;

Abstract
Using (r, s)-preopen sets [14] and pre-$\small{{\omega}_t}$-closures [6], a new kind of covering property $\small{P^t_{({\omega}_r,s)}}$-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-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-cluster sets and (r, s)t-$\small{{\theta}_f}$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-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 $\small{P^t_{({\omega}_r,s)}}$-closedness has also been established in terms of pre-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-cluster sets.
Keywords
pre-$\small{\omega}$-closure;$\small{\theta}$-closure;pre-($\small{{\omega}_r}$, s)-open;$\small{P^t_{({\omega}_r,s)}}$-closed;$\small{P^t_{(r,s)}}$-closed;($\small{{\omega}_r}$, s)t-regular;pre-($\small{{\omega}_r}$, s)-$\small{{\theta}_t}$-complete adherent;pre-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-cluster set;(r, s)t-$\small{{\theta}_f}$-precluster set;pre-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-irresolute;strongly pre-($\small{{\omega}_r}$, s)t-$\small{{\theta}_f}$-continuous;(r, s)f-preopen;pairwise (r, s)-Urysohn;almost regular;
Language
English
Cited by
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