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

Year 2015, Volume: 44 Issue: 6, 1411 - 1426, 01.12.2015

A.l. Pinchuck G. Jager

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

References

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