A new ordered compactification

D. C. Kent and T. A. Richmond

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

Abstract:

A new Wallman-type ordered compactification γ ∘ X is constructed using maximal C Z -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 R n . It is shown that γ ∘ X is always T 1 , but can fail to be T 1 -ordered or T 2 .

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:767910

DOI: 10.1155/S0161171293000146

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