A class of completely regular spaces
In this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson's compactification of convergence spaces. We also prove a non-existance of a dense convergence space compac...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117128400020X |
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| _version_ | 1832547497822650368 |
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| author | Patrik E. Eklund |
| author_facet | Patrik E. Eklund |
| author_sort | Patrik E. Eklund |
| collection | DOAJ |
| description | In this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson's compactification of convergence spaces. We also prove a non-existance of a dense convergence space compactification with lifting property. |
| format | Article |
| id | doaj-art-3c1349e891224647b1e31d73af21ce38 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3c1349e891224647b1e31d73af21ce382025-02-03T06:44:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017119720010.1155/S016117128400020XA class of completely regular spacesPatrik E. Eklund0Department of Mathematics, Åbo Akademi, Åbo 50 20500, FinlandIn this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson's compactification of convergence spaces. We also prove a non-existance of a dense convergence space compactification with lifting property.http://dx.doi.org/10.1155/S016117128400020Xconvergence spacecompactification. |
| spellingShingle | Patrik E. Eklund A class of completely regular spaces International Journal of Mathematics and Mathematical Sciences convergence space compactification. |
| title | A class of completely regular spaces |
| title_full | A class of completely regular spaces |
| title_fullStr | A class of completely regular spaces |
| title_full_unstemmed | A class of completely regular spaces |
| title_short | A class of completely regular spaces |
| title_sort | class of completely regular spaces |
| topic | convergence space compactification. |
| url | http://dx.doi.org/10.1155/S016117128400020X |
| work_keys_str_mv | AT patrikeeklund aclassofcompletelyregularspaces AT patrikeeklund classofcompletelyregularspaces |