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Some Topologies Induced by b-open Sets
El-Monsef, M.E. Abd,El-Atik, A.A.,El-Sharkasy, M.M. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
The class of b-open sets in the sense of $Andrijevi{\acute{c}}$ ([3]), was discussed by El-Atik ([9]) under the name of ${\gamma}-open$ sets. This class is closed under arbitrary union. The aim of this paper is to use ${\Lambda}-sets$ and ${\vee}-sets$ due to Maki ([15]) some topologies are constructed with the concept of b-open sets. $b-{\Lambda}-sets,\;b-{\vee}-sets$ are the basic concepts introduced and investigated. Moreover, several types of near continuous function based on $b-{\Lambda}-sets,\;b-{\vee}-sets$ are constructed and studied.
On Separation Axioms in Fuzzifying Bitopological Spaces
Ahmed Abd El-Monsef Allam,Ahmed Mohammed Zahran,Ahmed Khalf Mousa,Hana Mohsen Binshahnah 한국지능시스템학회 2020 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.20 No.1
In present paper, we introduce and study the concepts of T₀<SUP>(i;j)</SUP>-, T₁<SUP>(i;j)</SUP> -, T₂<SUP>(i;j)</SUP>(pairwise Hausdorff)-, TR<SUP>(i;j)</SUP> (pairwise regularity)-, TN<SUP>(i;j)</SUP> (pairwise normality)-, R₀<SUP>(i;j)</SUP>-, R₁<SUP>(i;j)</SUP>-, T₃<SUP>(i;j)</SUP> - and T₄<SUP>(i;j)</SUP> - separation axioms in fuzzifying bitopological spaces and study some relations between them. Also we investigate the image of these kinds of fuzzifying bitopological spaces under some types of fuzzy mappings.