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26 April 2024

» arxiv » math.GN/0505484

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Translation-invariant generalized topologies induced by probabilistic norms
Bernardo Lafuerza-Guillen ; Jose L. Rodriguez ;
Date:	23 May 2005
Subject:	General Topology; Probability MSC-class: 54E70; 46S50 \| math.GN math.PR
Abstract:	In this paper we consider probabilistic normed spaces as defined by Alsina, Sklar, and Schweizer, but equipped with non necessarily continuous triangle functions. Such spaces endow a generalized topology that is Fréchet-separable, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable.
Source:	arXiv, math.GN/0505484
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