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Categorical Properties of Probabilistic Convergence Spaces

Applied Categorical Structures, 1998
It is proved that the category of probabilistic pretopological (or pseudotopological) spaces is the extensional topological hull (or cartesian-closed extensional topological hull, resp.) of the category \(F_T\)-diagonal probabilistic convergence spaces for any triangular norm \(T\).
Herrlich, Horst, Zhang, Dexue
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Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces

Applied Categorical Structures, 1997
It is shown that the category CAP of convergence approach spaces is isomorphic to the category LTS of limit tower spaces. CAP has, as objects, pairs \((X,\lambda)\), where \(X\) is a set and \(\lambda:F(X)=\) (the set of filters on \(X)\to[0, \infty]^X\) satisfies (1) \(\lambda(\dot x)(x)=0\), where \(\dot x\) is the filter generated by \(\{x\}\), and ...
Brock, Paul, Kent, D. C.
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Probabilistic uniform convergence spaces redefined

Acta Mathematica Hungarica, 2015
Probabilistic uniform convergence spaces form a generalization of both uniform convergence spaces and probabilistic uniform spaces. In this paper the authors develop a theory of probabilistic uniform convergence spaces based on Tardiff's neighbourhood systems for probabilistic metric spaces. The generalization solves two problems.
Ahsanullah, T. M. G., Jäger, G.
openaire   +2 more sources

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