Ordered compactifications of products of two totally ordered spaces
type: Item
instance of: scholarly article
title: Ordered compactifications of products of two totally ordered spaces
zbMATH Open document ID: 0957.54014
DOI: 10.1023/A:1006328010276
author: Douglas D. Mooney
author: Thomas Richmond
published in: Order
publication date: 2000-07-24T00:00:00Z
review text: Let \(X\) and \(Y\) be totally ordered sets, and consider their totally ordered product \(X\times Y\). In this paper the authors study the semilattice of ordered compactifications of \(X\times Y\) smaller than \(\beta_0 X\times \beta_0 Y\). Here \(\beta_0 X\) is the Čech-Stone ordered- or Nachbin-compactification of \(X\). Similarly for \(Y\). For a totally ordered space \(Z\), let \(\sigma Z\) denote the smallest ordered compactification of \(X\). The authors prove results of the following nature. Suppose \(X\) and \(Y\) are totally ordered spaces having no simple singularities. Then \(\sigma X \times \sigma Y\) is the smallest ordered compactification of \(X\times Y\) less than \(\beta_0 X \times \beta_0 Y\). They are also able to characterize the semilattice of ordered compactifications in certain situations.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 06F30
zbMATH DE Number: 1463096
MaRDI profile type: Publication
full work available at URL: a:1006328010276
OpenAlex ID: W1124433
description: scientific article; zbMATH DE number 1463096