| Title:
|
Probabilistic approach spaces (English) |
| Author:
|
Jäger, Gunther |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
277-298 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
approach space |
| Keyword:
|
probabilistic approach space |
| Keyword:
|
probabilistic convergence space |
| Keyword:
|
probabilistic metric space |
| MSC:
|
54A20 |
| MSC:
|
54E70 |
| MSC:
|
54E99 |
| MSC:
|
60B99 |
| idZBL:
|
Zbl 06770146 |
| idMR:
|
MR3695467 |
| DOI:
|
10.21136/MB.2017.0064-15 |
| . |
| Date available:
|
2017-08-31T12:40:54Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146826 |
| . |
| Reference:
|
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