Abstract
In the class of fuzzy neighborhood spaces we demonstrate which implications hold and give counterexamples to the implications which do not hold between the notions of compactness, α-compactness, strong compactness and ultra compactness.
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CHANG C.L.: Fuzzy topological spaces, J. Math. Anal. Appl.24, 182–190 (1968)
GANTNER T.E., STEINLAGE R.C. and WARREN R.H.: Compactness in fuzzy topological spaces, J. Math. Anal. Appl.62, 547–562 (1978)
GOGUEN J.A.: The fuzzy Tychonoff theorem, J. Math. Anal. Appl.43, 734–742 (1973)
HOHLE U.: Probabilistische Topologien, Manuscripta Mathematica26, 223–245 (1978)
—: Probabilistisch kompakte L-unscharfe Mengen, Manuscripta Mathematica26, 331–347 (1979)
LOWEN R.: Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl.56, 621–633 (1976)
—: A comparison of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl.64, 446–454 (1978)
—: Convergence in fuzzy topological spaces, General Topology and its Applications10, 147–160 (1979)
—: Fuzzy uniform spaces, J. Math. Anal. Appl.82, 370–385 (1981)
—: Fuzzy neighborhood spaces, J. Fuzzy Sets and Systems7, 165–189 (1982)
WONG C.K.: Covering properties of fuzzy topological spaces, J. Math. Anal. Appl.43, 697–704 (1973)
ZADEH L.A.: Fuzzy Sets, Inf. Contr.8, 338–353 (1965)
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Lowen, R. Compactness notions in fuzzy neighborhood spaces. Manuscripta Math 38, 265–287 (1982). https://doi.org/10.1007/BF01170927
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DOI: https://doi.org/10.1007/BF01170927