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Maximal fuzzy topologies. (English) Zbl 0856.54004
Summary: We introduce and study maximal fuzzy $$P$$-spaces where $$P$$ is fuzzy Lindelöf, fuzzy countably compact, fuzzy compact, fuzzy lightly compact or fuzzy strongly compact. Characterizations are given for maximal fuzzy $$P$$-spaces where $$P$$ is fuzzy Lindelöf, fuzzy countably compact, fuzzy compact, or fuzzy strongly compact. A necessary condition is given for maximal fuzzy lightly compact spaces and fuzzy connected spaces.

##### MSC:
 54A40 Fuzzy topology 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
##### Keywords:
maximal fuzzy $$P$$-spaces
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##### References:
 [1] A. S. Bin Shahna: On fuzzy compactness and fuzzy Lindelofness. Bull. Calcutta Math. Soc. 83 (1991), 146-150. · Zbl 0764.54005 [2] A. B. Raha: Maximal topologies. J. Austral. Math. Soc. 8 (1968), 700-705. · Zbl 0165.25302 [3] K. K. Azad: On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity. J. Math. Anal. Appl. 82 (1981), 14-32. · Zbl 0511.54006 · doi:10.1016/0022-247X(81)90222-5 [4] G. Balasubramanian: On extensions of fuzzy topologies. Kybernetika 28 (1992), 3, 239-244. · Zbl 0795.54011 · www.kybernetika.cz · eudml:27740 [5] C. L. Chang: Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182-190. · Zbl 0167.51001 · doi:10.1016/0022-247X(68)90057-7 [6] U. V. Fatteh, D. S. Bassan: Fuzzy connectedness and its stronger forms. J. Math. Anal. Appl. 111 (1985), 440-464. · Zbl 0588.54008 · doi:10.1016/0022-247X(85)90229-X [7] S. Ganguly, S. Saha: A note on compactness in a fuzzy setting. Fuzzy Sets and Systems 34 (1990), 117-124. · Zbl 0689.54002 · doi:10.1016/0165-0114(90)90131-O [8] R. Lowen: Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56 (1976), 621-633. · Zbl 0342.54003 · doi:10.1016/0022-247X(76)90029-9 [9] S. Nanda: Strongly compact fuzzy topological spaces. Fuzzy Sets and Systems 42 (1991), 259-262. · Zbl 0736.54003 · doi:10.1016/0165-0114(91)90151-F
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