Geodesic
Probabilistic approach spaces
Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 277-298
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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.
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.
DOI : 10.21136/MB.2017.0064-15
Classification : 54A20, 54E70, 54E99, 60B99
Keywords: approach space; probabilistic approach space; probabilistic convergence space; probabilistic metric space 
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Jäger, Gunther. Probabilistic approach spaces. Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 277-298. doi: 10.21136/MB.2017.0064-15

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