Authors:
Md. Sahadat Hossain,Md. Saiful Islam,Mousumi Akter,DOI NO:
https://doi.org/10.26782/jmcms.2023.08.00001Keywords:
Fuzzy bitopological space,Regular space,FP-Continuous,FP – Open,FP – Close Map,Abstract
This paper introduced four notions of Fuzzy pairwise regular (in short FP-R) bitopological spaces and established some relation among them. Also, prove that all of these definitions satisfy the “good extension” property. Further, prove that all of these notions are hereditary. Finally, observe that all concepts are preserved under one-one, onto, and continuous mapping.Refference:
I. Abu Safiya A.S., Fora A.A. and Warner M.W., Fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces; Fuzzy sets and system. 62(1994), 367-373.
II. Abu Safiya A.S., Fora A.A. and Warner M.W., Higher separation axioms in bifuzzy topological spaces; Fuzzy sets and system. 79(1996), 367-373.
III. Amin M.R., Hossain M.S. and Miah S.S., Fuzzy Pairwise Regular Bitopological Spaces in Quasi-coincidence Sense; J. Bangladesh Academy of Science. 44(2) (2021), 139-143.
IV. Banerjee G. K., On pairwise almost strongly -continuous mapping; Bull. Cal. Math. Soc. 79(1987)314-320.
V. Chang C.L., Fuzzy topological spaces; J. Math. Anal Appl. 24(1968), 182-192.
VI. Das N.R. and Baishya, Fuzzy bitopological spaces and separation axioms; The Jour. Fuzzy Math. 2(1994), 389 – 396.
VII. Demirci M., Category-theoretic fuzzy topological spaces and their dualites; Fuzzy sets and systems. 227(2013) 1-24.
VIII. Garcia J.G., Romaguera S. and Sanehis M., An identification theorem for the completion of the Hausdorff fuzzy metric; Fuzzy sets and systems. 227(2013) 96-106.
IX. Islam M.S., Islam R. and Islam M.S. “On a study on Intuitionistic fuzzy r-normal Spaces” Notes on Intuitionistic Fuzzy Sets27(3)(2021),69-82
X. Hossain M. S. and Ali D.M. ; On Fuzzy Regular Topological Spaces. Rajshahi University Studies Part-B, Journal of Science, Vol. 34 (2006), 25-36.
XI. Hutton B. and Reilly I, Separation axioms in fuzzy topological spaces. Fuzzy Sets and Systems 3(1980) 93-104.
XII. Kandil A. and El-Etriby A.M., On separation axioms in fuzzy topological spaces. Tamkang J. Math. 18(1987) 49-59.
XIII. Kandil A. and El-Shafee M.E., Separation axioms for fuzzy bitopological space; J. Inst. math. Comput. Sci. 4(3) (1991) 373-383.
XIV. Kandil A., Nouh A.A. and El-Sheikkh S.A., On fuzzy bitopological spaces; Fuzzy sets and systems. 74(1995) 353-63.
XV. Kelly J.C., Bitopological Spaces,Proc. London math. Soc. 13(3) (1963) 71-89.
XVI. Kim Y.C., r- fuzzy semi – open sets in fuzzy bitopological spaces, J. Math. Sci. Special (FJMS) II (2000) 221-236.
XVII. Kumar S.S., On fuzzy pairwise - Continuity and fuzzy pairwise precontinuity. Fuzzy Sets and Systems 62(1994) 232-238.
XVIII. Lee E.P., Preopen sets in smooth bitopological spaces. J. Com. Korean Math. Soc. 18(3)(2003) 521-532.
XIX. Lowen R., Fuzzy topological spaces and fuzzy compactness; J. Math. Anal. Appl. 56(1976), 621-633.
XX. Lowen R. and Srivastava A.K., FTS0 : The epireeflective hull of the sierpinski object in FTS; Fuzzy sets and system. 29 (1989) 171-76.
XXI. Mahbub M.A., Hossain M.S. and Hossain M.A. “Para-Compactness concept in intuitionistic fuzzy topological spaces” J. Mech. Cont. & Math. Sci., 17(4)(2022), 32-39.
XXII. Mukherjee A., Completely induced bifuzzy topological spaces. Indian J. pure appl Math. 33(6) (2002)911-916.
XXIII. Nouh A.A., On separation axioms in fuzzy bitopological spaces; Fuzzy sets and systems 80(1996)225-236.
XXIV. Prova T.T. and Hossain M.S., Separation axioms in intuitionistic topological spaces; Italian Journal of Pure and Applied Mathematics, N.48 (2022) 986-995.
XXV. Prova T.T. and Hossain M.S. “Intuitionistic fuzzy based regular and normal spaces” Notes on Intuitionistic Fuzzy Sets26(4)(2020),53-63.
XXVI. Ramadan A.A, Abbas S.E. and Abdel – Latif A.A. , On fuzzy bitopological spaces in Sostaks sense; J. Commun Korean Math. Soc. 21(2006), No 3, 497-514.
XXVII. Weiss M.D., Fixed points , separation and induced topologies for fuzzy sets. J. Math . Anal . Appl . 50 (1975), 142-150.
XXVIII. Wong C.K. , Fuzzy points and local properties of Fuzzy topology ; J. Math. Anal . Appl. 46 (1974), 316-328.
XXIX. Yue Y., Lattice –valued induced fuzzy topological spaces. Fuzzy sets and systems 158(2007) 1461-1471.
XXX. Zadeh L.A., Fuzzy sets. Information and control 8 (1965). 338-353.