P^{t}_{(ωr,s)}-CLOSED SPACES AND PRE-(ω_{r},s)t-θ_{f}-CLUSTER SETS

- Journal title : Communications of the Korean Mathematical Society
- Volume 26, Issue 1, 2011, pp.135-149
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2011.26.1.135

Title & Authors

P^{t}_{(ωr,s)}-CLOSED SPACES AND PRE-(ω_{r},s)t-θ_{f}-CLUSTER SETS

Afsan, Bin Mostakim Uzzal; Basu, Chanchal Kumar;

Afsan, Bin Mostakim Uzzal; Basu, Chanchal Kumar;

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.

Keywords

pre--closure;-closure;pre-(, s)-open;-closed;-closed;(, s)t-regular;pre-(, s)--complete adherent;pre-(, s)t--cluster set;(r, s)t--precluster set;pre-(, s)t--irresolute;strongly pre-(, s)t--continuous;(r, s)f-preopen;pairwise (r, s)-Urysohn;almost regular;

Language

English

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