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...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2017-10-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/142/3/mb142_3_4.pdf |
| Summary: | 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. |
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| ISSN: | 0862-7959 2464-7136 |