On the isomorphy of categories of probabilistic limit spaces under t-norms

Authors : A. L. Pinchuck, G. Jager

Pages : 1411-1426

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Publication Date : 2015-12-01

Article Type : Research

Abstract :We show that for the classes of strict t-norms, the categories of probabilistic limit spaces under these t-norms are all isomorphic to each other. The same is true for the categories of probabilistic limit spaces under nilpotent t-norms. To show this, we study the isomorphisms be- tween the categories of probabilistic limit spaces under a t-norm, limit tower spaces and approach limit spaces. Similar results are obtained for probabilistic Cauchy spaces and probabilistic uniform limit spaces. 
Keywords : Probabilistic limit space, probabilistic uniform limit space, proba- bilistic Cauchy space, limit tower space, uniform limit tower space, Cauchy tower space, convergence approach space, approach Cauchy space, approach uniform limit space, t-norm