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Get Access to Full TextWe define probabilistic convergence groups based on Tardiff’s neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as probabilistic limit groups under a t-norm as defined earlier by the authors. We further show that a probabilistic convergence group induces a natural probabilistic uniform convergence structure and give a result on probabilistic metrization.
MSC 2010: Primary 54A20; 54B30; 54E15; 54E36; 54E70; 54H11
Keywords: probabilistic metric space; distance distribution function; profile function; Tardiff-neighborhood system; probabilistic convergence space; probabilistic uniform convergence space; probabilistic convergence group; probabilistic uniformization; probabilistic metric group; probabilistic normed group; probabilistic metrization; category theory
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Received: 2015-04-13
Accepted: 2016-04-11
Published Online: 2017-07-14
Published in Print: 2017-08-28
Citation Information: Mathematica Slovaca, Volume 67, Issue 4, Pages 985–1000, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0027.
© 2017 Mathematical Institute Slovak Academy of Sciences.
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