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Probabilistisch kompakte L-unscharfe Mengen

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Abstract

In the case of completely distributive lattices (L,≤) we establish a probabilistic version of Alexander's subbase lemma and of Tychonoff's theorem for L-fuzzy sets. As an application we obtain that probabilistic topologies induced by compact ordinary topologies are also compact; i.e. ordinary compactness is consistent with probabilistic compactness. Regarding the validity of these results a counterexample shows that the complete distributivity of (L,≤) cannot be replaced by a weaker distributivity condition.

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Authors and Affiliations

  1. Fachbereich Mathematik der Gesamthochschule Wuppertal, Gaußstr. 20, D-5600, Wuppertal 1, Bundesrepublik Deutschland

    Ulrich Höhle

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  1. Ulrich Höhle
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Höhle, U. Probabilistisch kompakte L-unscharfe Mengen. Manuscripta Math 26, 331–347 (1979). https://doi.org/10.1007/BF01170258

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  • DOI: https://doi.org/10.1007/BF01170258

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