Degeneracy of some cluster sets

C.K. Basu; B.M. Uzzal Afsan; S.S. Mandal

Degeneracy of some cluster sets

Autori

C.K. Basu West Bengal State University - Department of Mathematics
B.M. Uzzal Afsan Sripat Singh College - Department of Mathematics
S.S. Mandal Krishnagar Women's College - Department of Mathematics

Parole chiave:

β-open, β-closure, θ-closure, δ-closure, β-closed space, β-θ-cluster set, β-δ-cluster set, weakly Hausdorff, Urysohn

Abstract

Using θ-closure [39], δ-closure [39] of a subset and β-open [1] sets, we initiate two new kinds of cluster sets for functions and multifunctions. An explicit expression of each kind of cluster sets are given in terms of ¯lters and grills [38] and also several of their properties are investigated. In the process, the degeneracy of such cluster sets are used as tools to obtain new characterizations of various separation axioms. As application, such investigations ultimately provide new techniques for studying the covering property β-closedness [7].

Cover of n°28 Italian Journal of Pure and Applied Mathematics

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Pubblicato

2011-07-19

Come citare

Basu, C., Uzzal Afsan, B., & Mandal, S. (2011). Degeneracy of some cluster sets. Italian Journal of Pure and Applied Mathematics, 28, 63–78. Recuperato da https://journals.uniurb.it/index.php/ijpam/article/view/6014