Normal Separation Axiom on Fuzzy Bitopological Space
Keywords:
Fuzzy Bitopological Space, Fuzzy Normal Bitopological Space, Good Extension, Mappings, Quasi-coincidenceAbstract
In our paper, we present three novel concepts related to the normal separation property within the realm of fuzzy bitopological spaces (FPTS), specifically focusing on pairwise fuzzy normal bitopological spaces (FPN). These notions are introduced in a quasi-coincidence sense, and we establish relationships between our propositions and other existing ones. Furthermore, we provide proofs demonstrating that all the introduced concepts exhibit the ‘good extension’ property. Notably, we observe that our notions maintain their characteristics under one-one, onto, fuzzy pairwise open (FP-open), fuzzy closed (FP-closed), and fuzzy pairwise continuous (FP-continuous) mappings.
References
Ali, D. M. (1990a). A note on fuzzy regularity concepts. Fuzzy Sets and Systems, 35, 101-104.
Ali, D. M. (1990b). On certain separation and connectedness concepts in fuzzy topology, PhD, Banaras Hindu University, India.
Ahmd, F. A. (1989). Separations axioms for fuzzy spaces. Fuzzy Sets and Systems, 33, 59-75.
Amin, M. R., Ali, D. M., & Hossain, M. S. (2014). On T0 fuzzy bitopologicalspaces. Journal of Bangladesh cademy of Sciences, 32(2), 209- 217.
Chang, C. L. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Application, 24, 182-192.
Goguen, T. A. (1973). Fuzzy Tychonoff theorem. Journal of Mathematical Analysis and Application, 43, 734-742.
Guler, A. C., & Kale, G. (2015). Regularity and normality in soft ideal topological spaces. Anals of Fuzzy Mathematics and Informatics, 9(3), 373-383.
Hossain, M. S., & Ali, D. M. (2007). On T1 fuzzy bitopological spaces. Journal of Bangladesh Academy of Sciences, 31, 129-135.
Hutton, B. (1975). Normality in fuzzy topological spaces. Journal of Mathematical Analysis and Application, 50, 74-79.
Kandil, & El-Shafee (1991). Separation axioms for fuzzy bitopological spaces. J. Inst. Math. Comput. Sci. 4(3), 373-383.
Kandil, A., Nouh, A. A., & El-Sheikkh, S. A. (1995). On fuzzy bitopological spaces. Fuzzy sets and systems. 74, 353-363.
Kelly, J. C. (1963). Bitopological Spaces, Proc. London math. Soc. 13(3), 71-89.
Lowen, R. (1976). Fuzzy topological spaces and fuzzy compactness. Journal of Mathematical Analysis and Application, 56, 621-633.
Malghan, S. R., & Benchalli, S. S. (1984). On open maps, closed maps and local compactness in fuzzy topological spaces. Journal of Mathematical Analysis and Application, 99(2), 338-349.
Ming, P. P., & Ming, L. Y. (1980a). Fuzzy topology I. neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Application, 76, 571-599.
Ming, P. P., & Ming, L. Y. (1980b). Fuzzy topology II. product and quotient spaces. Journal of Mathematical Analysis and Application, 77, 20-37.
Miah, S. S., & Amin, M. R. (2017a). Mappings in fuzzy Hausdorff spaces in quasi-coincidence sense. Journal of Bangladesh Academy of Sciences, 41(1), 47-56.
Miah, S. S., & Amin, M. R. (2017b). Certain properties on fuzzy R0 topological spaces in quasi-coincidence sense. Annals of Pure and Applied Mathematics, 14(1), 125-131.
Miah, S. S., Amin, M. R., & Jahan, M. (2017a). Mappings on fuzzy T0 Topological Spaces in Quasi-coincidence
Sense. Journal of Mathematical and Computational Science, 7(5), 883-894.
Miah, S. S., Amin, M. R., & Rashid, H. (2017b). T1–type Separation on Fuzzy Topological Spaces in Quasicoincidence Sense. Journal of Mechanics of Continua and MathematicalSciences, 12(1), 45-56.
Miah, S. S., Amin, M. R., & Rana, S. (2018). Fuzzy normal topological space in quasi-coincidence sense. J. Bangladesh Acad. Sci. 42(2), 201-205.
Miah, S. S., Amin, M. R., & Hoque, M. F. (2019a). Separation axioms (T1) on fuzzy bitopological space in quasi-coincidence sense. International J. Math. Combin. 3(2019), 43-53.
Miah, S. S., Jahan, M., & Amin, M. R. (2019b). Separation axiom (Hausdorff) on fuzzy bitopological space in quasi-coincidence sense. J. Sci. Eng. Res., 6(4), 167-174.
Safiya, A. S. A., Fora, A. A., & Warner, M. W. (1994). Fuzzy Separation axioms and fuzzy continuity in bitopological spaces. Fuzzy Sets and Systems 62, 367-373.
Warren, R. H. (1974). Continuity of mappings in fuzzy topological spaces, Notices A.M. S. 21, A-451. Wong, C. K. (1974). Fuzzy topology: product and quotient theorem. Journal of Mathematical Analysis and Application, 45, 512-521.
Wuyts, P., & Lowen, R. (1983). On separation axioms in fuzzy topological spaces, fuzzy neighborhood spaces,
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