Abstract
Basic properties of probabilistic topologies associated with L-fuzzy uniformities are studied, e.g. regularity, uniform continuity and 1-completeness. The main result is the existence and uniqueness of the probabilistic completion of L-fuzzy uniform spaces. Moreover with respect to the applicability of this theory we also give concrete representations of the probabilistic completion of compact as well as of Polish spaces.
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Höhle, U. Probabilistic topologies induced by L-fuzzy uniformities. Manuscripta Math 38, 289–323 (1982). https://doi.org/10.1007/BF01170928
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DOI: https://doi.org/10.1007/BF01170928