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

Authors : Al PİNCHUCK, G JAGER

Pages : 1411-1426

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Publication Date : 2015-12-01

Article Type : Research Paper

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