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Start Over Subject probabilistic metric space

2. Probabilistic approach spaces

Creator:
Jäger, Gunther
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
approach space, probabilistic approach space, probabilistic convergence space, and probabilistic metric space
Language:
English
Description:
We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to a simultaneously bireflective and bicoreflective subcategory and that the category of probabilistic quasi-metric spaces is isomorphic to a bicoreflective subcategory of the category of probabilistic approach spaces.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public