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Keywords:
fuzzy proper function; smooth fuzzy topology; smooth fuzzy continuity
fuzzy proper function; smooth fuzzy topology; smooth fuzzy continuity
Summary:
In this paper, we introduce the notion of the $(\alpha ,\beta )$-weakly smooth fuzzy continuous proper function and discuss its properties. We also study several notions of connectedness in smooth fuzzy topological spaces and establish that the product of connected sets (spaces) is not connected in any sense, as well as investigate continuous images of smooth connected sets (spaces) under $(\alpha ,\beta )$-weakly smooth fuzzy continuous functions.
References:
[1] Aygün, H., Abbas, S. E.: Some good extensions of Šostak's L-fuzzy topology. Hacet. J. Math. Stat. 36 (2007), 115-125. MR 2411629
[2] Abbas, S. E.: On smooth fuzzy subspaces. Int. J. Math. Math. Sci. 66 (2004), 3587-3602. DOI 10.1155/S0161171204401021 | MR 2128776 | Zbl 1071.54002
[3] Chakraborty, M. K., Ahsanullah, T. M. G.: Fuzzy topology on fuzzy sets and tolerance topology. Fuzzy Sets Syst. 45 (1992), 103-108. MR 1148457 | Zbl 0754.54004
[4] Chang, C. L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182-189. DOI 10.1016/0022-247X(68)90057-7 | MR 0236859 | Zbl 0167.51001
[5] Chaudhuri, A. K., Das, P.: Some results on fuzzy topology on fuzzy sets. Fuzzy Sets Syst. 56 (1993), 331-336. MR 1227903 | Zbl 0794.54012
[6] Demirici, M.: On several types of compactness in smooth topological spaces. Fuzzy Sets Syst. 90 (1997), 83-88. MR 1460342
[7] Demirici, M.: Neighborhood structures of smooth topological spaces. Fuzzy Sets Syst. 92 (1997), 123-128. MR 1481022
[8] Demirici, M.: Three topological structures of smooth topological spaces. Fuzzy Sets Syst. 101 (1999), 185-190. MR 1658916
[9] Gayyar, M. K. El, Kerre, E. E.: Almost compactness and near compactness in smooth topological spaces. Fuzzy Sets Syst. 62 (1994), 193-202. MR 1274998 | Zbl 0833.54007
[10] Alla, M. A. Fath, Mahmoud, F. S.: Fuzzy topology on fuzzy sets, functions with fuzzy closed graphs, strong fuzzy closed graphs. J. Fuzzy Math. 9 (2001), 525-533. MR 1859535
[11] Guido, C.: Powerset operators based approach to fuzzy topologies on fuzzy sets, topological and algebraic structures in fuzzy sets. A handbook of recent developments in the Mathematics of fuzzy sets S. E. Rodabaugh and E. P. Klement Trends Log. Stud. Log. Libr., vol. 20, Kluwer Academic Publishers, Dordrecht (2003), 401-413. MR 2046750
[12] Hazra, R. N., Samanta, S. K., Chattopadhyay, K. C.: Fuzzy topology redefined. Fuzzy Sets Syst. 45 (1992), 79-82. MR 1148454 | Zbl 0756.54002
[13] Höhle, U.: Upper semicontinuous fuzzy sets and applications. J. Math. Anal. Appl. 78 (1980), 659-673. DOI 10.1016/0022-247X(80)90173-0 | MR 0601561 | Zbl 0462.54002
[14] Höhle, U., (eds.), S. E. Rodabaugh: Mathematics of fuzzy Sets: Logic, Topology, and Measure Theory. Kluwer Academic Publishers, Dordrecht (1999). MR 1788899 | Zbl 0942.00008
[15] Höhle, U., Šostak, A. P.: A general theory of fuzzy topological spaces. Fuzzy Sets Syst. 73 (1995), 131-149. MR 1355360 | Zbl 0948.54003
[16] Höhle, U., Šostak, A. P.: Axiomatic foundations of fixed-basis fuzzy topology. Mathematics of fuzzy Sets: Logic, Topology, and Measure Theory U. Höhle, S. E. Rodabaugh Kluwer Academic Publishers, Dordrecht (1999), 123-272. MR 1788903 | Zbl 0977.54006
[17] Kubiak, T.: On fuzzy topologies. Ph.D. thesis, Adam Mickiewicz University. Poznań, Poland (1985).
[18] Kubiak, T., Šostak, A. P.: Lower set-valued fuzzy topologies. Quaestiones Math. 20 (1997), 423-429. DOI 10.1080/16073606.1997.9632016 | MR 1641456 | Zbl 0890.54005
[19] Kubiak, T., Šostak, A. P.: Foundations of the theory of $(L,M)$-fuzzy topological spaces. Abstracts of the 30th Linz Seminar on Fuzzy Set Theory U. Bodenhofer, B. De Baets, E. P. Klement, S. Saminger-Platz Johannes Kepler Universität, Linz (2009), 70-73. MR 2819393
[20] Ming, P. P., Ming, L. Y.: Fuzzy topology, I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl. 76 (1980), 571-599. DOI 10.1016/0022-247X(80)90048-7 | MR 0587361
[21] Peeters, W.: Subspaces of smooth fuzzy topologies and initial smooth fuzzy structures. Fuzzy Sets Syst. 104 (1999), 423-433. MR 1692338 | Zbl 0944.54004
[22] Rodabaugh, S. E.: Categorical foundations of variable-basis fuzzy topology. Mathematics of fuzzy Sets: Logic, Topology, and Measure Theory U. Höhle, S. E. Rodabaugh Kluwer Academic Publishers, Dordrecht (1999), 273-388. MR 1788904
[23] Rodabaugh, S. E.: Powerset operator foundations for Poslat fuzzy set theories and topologies. Mathematics of fuzzy Sets: Logic, Topology, and Measure Theory U. Höhle, S. E. Rodabaugh Kluwer Academic Publishers, Dordrecht (1999), 91-116. DOI 10.1007/978-1-4615-5079-2_3 | MR 1788901 | Zbl 0974.03047
[24] Ramadan, A. A., Alla, M. A. Fath, Abbas, S. E.: Smooth fuzzy topology on fuzzy sets. J. Fuzzy Math. 10 (2002), 59-68. MR 1894600
[25] Roopkumar, R., Kalaivani, C.: Continuity of fuzzy proper function on Šostak's $I$-fuzzy topological spaces. Commun. Korean Math. Soc. 26 (2011), 305-320. DOI 10.4134/CKMS.2011.26.2.305 | MR 2816568
[26] Šostak, A. P.: On a fuzzy topological structure. Rend. Circ. Matem. Palermo Ser. II. 11 (1985), 89-103. MR 0897975
[27] Srivastava, R.: On separation axioms in a newly defined fuzzy topology. Fuzzy Sets Syst. 62 (1994), 341-346. MR 1276601 | Zbl 0833.54006
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