Mathematica Bohemica, Vol. 142, No. 3, pp. 277-298, 2017
Probabilistic approach spaces
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.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at email@example.com. Subscribers of Springer need to access the articles on their site, which is http://mb.math.cas.cz/.
Affiliations: Gunther Jäger, School of Mechanical Engineering, University of Applied Sciences Stralsund, Zur Schwedenschanze 15, 18435 Stralsund, Germany, e-mail: firstname.lastname@example.org