Uniformizable Cauchy spaces
A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy str...
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| Format: | Article |
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Hindawi Limited
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000489 |
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doaj-022c178666b64b2c8b51d31104deddc12020-11-24T23:18:33ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015351352710.1155/S0161171282000489Uniformizable Cauchy spacesEva Lowen-Colebunders0Vrije Universiteit Brussel, Departement Wiskunde, F7, Pleinlaan 2, Brussel 1050 , BelgiumA family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the filter u(C)=⋂F∈CF×F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems.http://dx.doi.org/10.1155/S0161171282000489uniformityCauchy spacecompletionCauchycontinuous maprealcompactnessCauchy covering system. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Eva Lowen-Colebunders |
| spellingShingle |
Eva Lowen-Colebunders Uniformizable Cauchy spaces International Journal of Mathematics and Mathematical Sciences uniformity Cauchy space completion Cauchy continuous map realcompactness Cauchy covering system. |
| author_facet |
Eva Lowen-Colebunders |
| author_sort |
Eva Lowen-Colebunders |
| title |
Uniformizable Cauchy spaces |
| title_short |
Uniformizable Cauchy spaces |
| title_full |
Uniformizable Cauchy spaces |
| title_fullStr |
Uniformizable Cauchy spaces |
| title_full_unstemmed |
Uniformizable Cauchy spaces |
| title_sort |
uniformizable cauchy spaces |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1982-01-01 |
| description |
A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the filter u(C)=⋂F∈CF×F is a uniformity and C is its collection of Cauchy filters. This problem is treated using Cauchy covering systems. |
| topic |
uniformity Cauchy space completion Cauchy continuous map realcompactness Cauchy covering system. |
| url |
http://dx.doi.org/10.1155/S0161171282000489 |
| work_keys_str_mv |
AT evalowencolebunders uniformizablecauchyspaces |
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1725581037188153344 |