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Construction of fuzzy topology by using fuzzy metric. (English) Zbl 1499.54047

Summary: In this work, we construct a stratified fuzzy topological space induced by a fuzzy metric in the sense of Kramosil and Michalek. Our special interests are to investigate bases for such spaces and to study continuity and compactness.

MSC:

54A40 Fuzzy topology
Full Text: DOI

References:

[1] T. Bag, S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems 151 (2005) 513-547. · Zbl 1077.46059
[2] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications 24 (1968) 182-190. · Zbl 0167.51001
[3] T. E. Gantner, R. C. Steinlage, R. H. Warren, Compactness in fuzzy topological spaces, Journal of Mathematical Analysis and Applications 62 (1978) 547-562. · Zbl 0372.54001
[4] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994) 395-399. · Zbl 0843.54014
[5] A. George, P. Veeramani, Some theorems in fuzzy metric spaces, Journal of Fuzzy Mathematics 3 (1995) 933-940. · Zbl 0870.54007
[6] V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000) 485-489. · Zbl 0985.54007
[7] V. Gregori, J. J. Minana, S. Morillas, A note on local bases and convergence in fuzzy metric spaces, Topology and its Applications 163 (2014) 142-148. · Zbl 1282.54008
[8] V. Gregori, S. Morillas, A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems 161 (2010) 2193-2205. · Zbl 1201.54011
[9] S. Grecova, A. Sostak, I. Uljane, A construction of a fuzzy topology from a strong fuzzy metric, Applied General Topology 17 (2016) -. · Zbl 1353.54009
[10] I. Kramosil, J. Mich´alek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975) 336-344. · Zbl 0319.54002
[11] R Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications 56 (1976) 621-633. · Zbl 0342.54003
[12] R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, Journal of Mathematical Analysis and Applications 64 (1978) 446-454. · Zbl 0381.54004
[13] J. J. Mi ˜nana, A. ˇSostak, Fuzzifying topology induced by a strong fuzzy metric, Fuzzy Sets and Systems 300 (2016) 24-39. · Zbl 1378.54012
[14] I. Mardones-Perez, M. A. Prada Vicente, Fuzzy pseudometric spaces vs fuzzifying structures, Fuzzy Sets and Systems 267 (2015) 117-132. · Zbl 1392.54013
[15] I. Mardones-Perez, M. A. Prada Vicente, A representation theorem for fuzzy pseudometrics, Fuzzy Sets and Systems 195 (2012) 90-99. · Zbl 1255.54014
[16] I. M. Saheli, Fuzzy Topology Generated by Fuzzy Norm, Iranian Journal of Fuzzy Systems 13 (2016) 113-123. · Zbl 1359.54009
[17] B. Schweizer, A. Sklar, Statistical metric spaces, Pac.J.Math 10 (1960) 314-334. · Zbl 0091.29801
[18] P. Wuyts, On the determination of fuzzy topological spaces and fuzzy neighborhood spaces by their level-topologies, Fuzzy Sets and Systems 12 (1984) 71-85. · Zbl 0574.54004
[19] P. Wuyts, On level-topologies and maximality of fuzzy topological spaces, Fuzzy Sets and Systems 79 (1996) 337-339. · Zbl 0869.54008
[20] Y. Yue, F. G. Shi, On fuzzy pseudo-metric spaces, Fuzzy Sets and Systems 161 (2010) 1105-1116 · Zbl 1194.54014
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