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On fuzzy bitopological spaces. (English) Zbl 0851.54010
Summary: We use the fuzzy topologies \(\tau_1\) and \(\tau_2\) to generate a family \(\tau_s\) which is a supra fuzzy topology on \(X\). Using the family \(\tau_s\), we introduce and study the concepts of separation axioms, continuity (resp. openness, closedness) of a mapping and compactness for a fuzzy bitopological space \((X, \tau_1, \tau_2)\). Our definitions preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces. We then investigate the relationship between these concepts and their correspondence with the fuzzy bitopological spaces [the first author and M. E. El-Shafee, Separation axioms for fuzzy bitopological spaces, J. Inst. Math. Comput. Sci., Math. Ser. 4, No. 3, 373-383 (1991)].

MSC:
54A40 Fuzzy topology
54E55 Bitopologies
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References:
[1] El-Shafee, M.E., Separation properties of Fbts’s, ()
[2] Engelking, R., General topology, (1977), PWN Warsaw
[3] Geping, W.; Lanfang, Hu., On induced fuzzy topological spaces, J. math. anal. appl., 108, 495-506, (1985) · Zbl 0578.54004
[4] Kandil, A.; El-Etriby, A.M., On separation axioms in fuzzy topological spaces, Tamkang J. math., 18, 49-59, (1987) · Zbl 0635.54004
[5] Kandil, A.; El-Shafee, M.E., Regularity axioms in fuzzy topological spaces and FR_{i}-proximities, Fuzzy sets and systems, 27, 217-231, (1988) · Zbl 0726.54006
[6] Kandil, A.; El-Shafee, M.E., Separation axioms for fuzzy bitopological spaces, J. inst. math. comput. sci., 4, 3, 373-383, (1991)
[7] Kandil, A.; EL-Sheikh, S.A.; Fawaz, H., On bitopological spaces, (), 115-132
[8] Kandil, A.; Gad, F., On fuzzy proximity spaces, Bull. fac. sci. assuit univ., 14, 2, 29-41, (1985)
[9] Lowen, R., Fuzzy topological spaces and compactness, J. math. anal. appl., 56, 621-633, (1976) · Zbl 0342.54003
[10] Lowen, R., A comparison of different compactness notions in fuzzy topological space, J. math. anal., 64, 446-454, (1978) · Zbl 0381.54004
[11] Mashhour, A.S.; Allam, A.A.; Mahmoud, F.S.; Khedr, F.H., On supratopological spaces, Indian J. pure appl. math., 14, 502-510, (1983) · Zbl 0511.54003
[12] Nouh, A.A., Some special mappings between fuzzy (bi)topological spaces, () · Zbl 0864.54003
[13] de Prada Vicente, M.A.; Macho Stadler, M., t-prefilter theory, Fuzzy sets and systems, 38, 115-124, (1990) · Zbl 0709.54003
[14] de Prada Vicente, M.A.; Macho Stadler, M., Strong separation and strong countability in fuzzy topological spaces, Fuzzy sets and systems, 43, 95-115, (1991) · Zbl 0760.54004
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