Vol. 66, No. 1, 1976

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Extensions of completely regular ordered spaces

Tae Ho Choe and Young Hee Hong

Vol. 66 (1976), No. 1, 37–48

In this paper we introduce the concept of o-completely regular filters on a completely regular ordered space in order to characterize compact ordered spaces and show that for any completely regular ordered space X, Nachbin compactification of X is precisely the strict extension of X with all maximal o-completely regular filters as the filter trace. With this concept, we also define k-compact ordered spaces for every infinite cardinal k, which give rise to a chain of extensive subcategories of the category of completely regular ordered spaces, analogous to the chain given by the category of k-compact spaces, for the different cardinals k.

Mathematical Subject Classification 2000
Primary: 54F05
Received: 23 October 1975
Revised: 29 April 1976
Published: 1 September 1976
Tae Ho Choe
Young Hee Hong