A new ordered compactification
A new Wallman-type ordered compactification γ∘X is constructed using maximal CZ-filters (which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A necessary and sufficient condition is given for γ∘X to coincide with the Nachbin compactification β∘X; in parti...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000146 |
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| _version_ | 1832547430261850112 |
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| author | D. C. Kent T. A. Richmond |
| author_facet | D. C. Kent T. A. Richmond |
| author_sort | D. C. Kent |
| collection | DOAJ |
| description | A new Wallman-type ordered compactification γ∘X is constructed using maximal CZ-filters
(which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A
necessary and sufficient condition is given for γ∘X to coincide with the Nachbin compactification β∘X; in
particular γ∘X=β∘X whenever X has the discrete order. The Wallman ordered compactification ω∘X
equals γ∘X whenever X is a subspace of Rn. It is shown that γ∘X is always T1, but can fail to be T1-ordered
or T2. |
| format | Article |
| id | doaj-art-549b26495d914f3d898cd2928a86d282 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-549b26495d914f3d898cd2928a86d2822025-02-03T06:44:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116111712410.1155/S0161171293000146A new ordered compactificationD. C. Kent0T. A. Richmond1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, WA, USADepartment of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USAA new Wallman-type ordered compactification γ∘X is constructed using maximal CZ-filters (which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A necessary and sufficient condition is given for γ∘X to coincide with the Nachbin compactification β∘X; in particular γ∘X=β∘X whenever X has the discrete order. The Wallman ordered compactification ω∘X equals γ∘X whenever X is a subspace of Rn. It is shown that γ∘X is always T1, but can fail to be T1-ordered or T2.http://dx.doi.org/10.1155/S0161171293000146CZ-setmaximal CZ-filterT1-ordered spaceT2-ordered spaceNachbin compactificationWallman ordered compactification. |
| spellingShingle | D. C. Kent T. A. Richmond A new ordered compactification International Journal of Mathematics and Mathematical Sciences CZ-set maximal CZ-filter T1-ordered space T2-ordered space Nachbin compactification Wallman ordered compactification. |
| title | A new ordered compactification |
| title_full | A new ordered compactification |
| title_fullStr | A new ordered compactification |
| title_full_unstemmed | A new ordered compactification |
| title_short | A new ordered compactification |
| title_sort | new ordered compactification |
| topic | CZ-set maximal CZ-filter T1-ordered space T2-ordered space Nachbin compactification Wallman ordered compactification. |
| url | http://dx.doi.org/10.1155/S0161171293000146 |
| work_keys_str_mv | AT dckent aneworderedcompactification AT tarichmond aneworderedcompactification AT dckent neworderedcompactification AT tarichmond neworderedcompactification |