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GENERALIZATIONS OF CLOSED FUNCTIONS IN SPACES WITH MINIMAL STRUCTURES


MARCELINA MOCANU
“Vasile Alecsandri” University of Bacău, Department of Mathematics and Informatics, Calea Mărășești 157, Bacău 600115, ROMANIA e-mail: mmocanu@ub.ro

Issue:

SSRSMI, Number 2, Volume XXXII

Section:

Volume 32, Number 2

Abstract:

Noiri and Popa introduced and studied the notion of M−closed function between spaces with minimal structures, developing a unified theory of modifications of closedness such as α−closedness, semi-closedness, preclosedness and β−closedness. Using a new notion, that of almost M- closed function, we extend the characterizations of M−closed functions proved by Popa and Noiri to spaces endowed with minimal structures not necessarily closed under arbitrary unions. These minimal structures are useful beyond General Topol-ogy. For bijections between spaces with minimal structure it turns out that almost M- closedness is equivalent to almost M−openness, both being equivalent to the M−continuity of the inverse function. Our main result generalizes a well-known theorem of Long and Herrington showing that θ−open sets in topological spaces are preserved by every function that is both open and closed.

Keywords:

minimal structure space, closure operator, almost M−open function, weakly M−open func-tion, m − θ−closure, boundary preservation.

Code [ID]:

SSRSMI202202V32S01A0004 [0005524]

Note:

Full paper:

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