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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |