A new ordered compactification
| Autor: | D. C. Kent, T. A. Richmond |
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| Jazyk: | angličtina |
| Rok vydání: | 1993 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 16, Iss 1, Pp 117-124 (1993) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 01611712 |
| DOI: | 10.1155/S0161171293000146 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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