Mathematica Bohemica, Vol. 142, No. 3, pp. 277-298, 2017
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.
Affiliations: Gunther Jäger, School of Mechanical Engineering, University of Applied Sciences Stralsund, Zur Schwedenschanze 15, 18435 Stralsund, Germany, e-mail: gunther.jaeger@fh-stralsund.de