×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: Link EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.