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 |
| Language: | English |
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Wiley
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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| _version_ | 1849687039724748800 |
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| author | Eva Lowen-Colebunders |
| author_facet | Eva Lowen-Colebunders |
| author_sort | Eva Lowen-Colebunders |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-022c178666b64b2c8b51d31104deddc1 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-022c178666b64b2c8b51d31104deddc12025-08-20T03:22:27ZengWileyInternational 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. |
| 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. |
| title | Uniformizable Cauchy spaces |
| title_full | Uniformizable Cauchy spaces |
| title_fullStr | Uniformizable Cauchy spaces |
| title_full_unstemmed | Uniformizable Cauchy spaces |
| title_short | Uniformizable Cauchy spaces |
| title_sort | uniformizable cauchy spaces |
| 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 |