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Probabilistic approach spaces

Gunther Jäger

Received October 22, 2015.   First published January 3, 2017.

Abstract: 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.

Keywords: approach space; probabilistic approach space; probabilistic convergence space; probabilistic metric space

Classification (MSC 2010): 54A20, 54E70, 54E99

DOI: 10.21136/MB.2017.0064-15

Full text available as PDF.

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