JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 51-56.doi: 10.6040/j.issn.1671-9352.0.2018.372

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RL-fuzzy topology and the related fuzzy compactness

LI Hong-yan1, LI Qing-hua2   

  1. 1. School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, Shandong, China;
    2. School of Mathematics and Information Science, Yantai University, Yantai 264005, Shandong, China
  • Published:2019-02-25

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Abstract: The concept of pseudo-complement on an L-subset A is defined and studied, where L is a completely distributive De Morgan algebra. Based on this new concept, the definition of RL-fuzzy topology on A is introduced. The L-fuzzy topology in sense of Kubiak and Šostak and the RL-topology on A are special cases of this kind of topology. The RL-fuzzy compactness of RL-fuzzy topological spaces is further studied. The union of two RL-fuzzy compact sets is RL-fuzzy compact. The intersection of an RL-fuzzy compact set and an RL-fuzzy closed set is RL-fuzzy compact. The RL-fuzzy compactness is an invariant under RL-fuzzy continuous maps.

Key words: RL-topology, RL-fuzzy topology, RL-fuzzy compactness, RL-fuzzy continuous

CLC Number: 

  • O141.1
[1] CHANG C. Fuzzy topological spaces[J]. J Math Anal Appl, 1968, 24(1):182-193.
[2] HÖHLE U. Upper semicontinuous fuzzy sets and applications[J]. J Math Anal Appl, 1980, 78(2):659-673.
[3] HÖHLE U. Probabilistic metrization of fuzzy uniformities[J]. Fuzzy Sets and Systems, 1982, 8(1):63-69.
[4] YING Mingsheng. A new approach to fuzzy topology(I)[J]. Fuzzy Sets and Systems, 1991, 39(3):303-321.
[5] KUBIAK T. On fuzzy topologies[D]. Poland: Adam Mickiewicz University, 1985.
[6] ŠOSTAK A. On a fuzzy topological structure[J]. Suppl Rend Circolo Matem Palermo, 1985, 11(11):89-103.
[7] FANG Jinming. I-FTOP is isomorphic to I-FQN and I-AITOP[J]. Fuzzy Sets and Systems, 2004, 147(2):317-325.
[8] FANG Jinming. Categories isomorphic to L-FTOP[J]. Fuzzy Sets and Systems, 2006, 157(6):820-831.
[9] 金秋,李令强. L-模糊远域空间与L-余模糊拓扑空间[J]. 山东大学学报(理学版), 2007, 42(9):119-121. JIN Qiu, LI Lingqiang. L-fuzzy remote neighborhood space and L-co-fuzzy topology space[J]. Journal of Shandong University(Natural Science), 2007, 42(9):119-121.
[10] YAO Wei. Moore-Smith convergence in (L,M)-fuzzy topology[J]. Fuzzy Sets and Systems, 2012, 190:47-62.
[11] 杨小飞. 模糊化拓扑空间的刻画[J]. 山东大学学报(理学版), 2016, 51(2):114-118. YANG Xiaofei. Characterization of L-fuzzifying topological spaces[J]. Journal of Shandong University(Natural Science), 2016, 51(2):114-118.
[12] ERCEG M. Functions, equivalence relations, quotient spaces, and subsets in fuzzy set theory[J]. Fuzzy Sets and Systems, 1980, 3(1):75-92.
[13] JÄGER G. Compactness and connectedness as absolute properties in fuzzy topological spaces[J]. Fuzzy sets and Systems, 1998, 94(3):405-410.
[14] RODABAUGH S. Separation axioms and the L-fuzzy real lines[J]. Fuzzy Sets and Systems, 1983, 11(1):163-183.
[15] DE MITRI C, GUIDO C. G-fuzzy topological spaces and subspaces[J]. Suppl Rend Circolo Matem Palermo, 1992, 29(29):363-383.
[16] DE MITRI C, GUIDO C. Some remarks on fuzzy powerset operators[J]. Fuzzy Sets and Systems, 2002, 126(2):241-251.
[17] GUIDO C. The subspace problem in the traditional point set context of fuzzy topology[J]. Quaestiones Math, 1997, 20(3):351-372.
[18] GUIDO C. Powerset operators based approach to fuzzy topologies on fuzzy sets[M] // RODABAUGH S E, KLEMENT E P. Topological and Algebraic Structures in Fuzzy Set. London: Kluwer Academic Publishers, 2003.
[19] FANG Jinming, GUO Yuanmei. Quasi-coincident neighborhood structure of relative I-fuzzy topology and its applications[J]. Fuzzy Sets and Systems, 2012, 190(1):105-117.
[20] FANG Jinming, GUO Yuanmei. Connectedness in Jager-Sostaks I-fuzzy topological spaces[J]. Proyecciones Journal of Mathematics, 2009, 28(3):219-236.
[21] WANG Guojun. Theory of topological molecular lattices[J]. Fuzzy Sets and Systems, 1992, 47(3):351-376.
[22] LIU Yingming, LUO Maokang. Fuzzy topology[M]. Singapore: World Scientific Publishing, 1997.
[23] KUDRI S, WARNER M. Some good L-fuzzy compactness-related concepts and their properties I[J]. Fuzzy Sets and Systems, 1995, 76(2):141-155.
[24] HÖHLE U, RODABAUGH S. Mathematics of fuzzy sets: logic, topology, and measure theory[M]. London: Kluwer Academic Publishers, 1999.
[25] SHI Fugui. A new definition of fuzzy compactness[J]. Fuzzy Sets and Systems, 2007, 158(13):1486-1495.
[26] LOWEN R. Fuzzy topological spaces and fuzzy compactness[J]. J Math Anal Appl, 1976, 56(3):621-633.
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