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Quaestiones Mathematicae 2003, 26 (2) : 125–140
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Completion of probabilistic uniform limit spaces
Authors:
H Nusser1
1Department of Mathematics, Free University of Berlin, Germany
Corresponding Author: H Nusser (E-mail: nusser@math.fu-berlin.de)
Abstract:
In this article completions of special probabilistic semiuniform convergence spaces are considered. It turns out that every probabilitic Cauchy space under a given t-norm T (triangular norm) has a completion which, in the special case of probabilistic Cauchy spaces with reference to T = min, coincides with the Kent-Richardson completion for probabilistic Cauchy spaces. Moreover, a completion of probabilistic uniform limit spaces T = min is given which in case of constant probabilistic uniform limit spaces coincides with the Wyler completion.
Mathematics Subject Classification (2000): 54A20, 54E15, 54D35
Keywords: Probabilistic semiuniform convergence spaces; (probabilistic) convergence spaces; (probabilistic) uniform limit spaces; (probabilistic) Cauchy spaces; completions; Wyler completion; Menger spaces; fuzzy uniformities
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