1. 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