Compact, separable, linearly ordered spaces
type: Item
instance of: scholarly article
title: Compact, separable, linearly ordered spaces
zbMATH Open document ID: 0889.54014
DOI: 10.1016/S0166-8641(97)00068-0
published in: Topology and its Applications
publication date: 1998-06-08T00:00:00Z
review text: A well-known question on monotonically normal spaces is whether each compact such space is the continuous image of a compact ordered space. This paper provides an affirmative answer for separable zero-dimensional spaces. The proof is a combinatorial and topological tour de force. In the meantime the author has improved the result, first by removing the assumption of zero-dimensionality [Zero-dimensionality and monotone normality, Topology Appl. 85, 319-333 (1998)] and more recently by relaxing separability to first-countability [Compact first countable linearly ordered spaces, http://www.unipissing.ca/topology/v/a/a/a/14.htm].
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1121476
zbMATH Keywords: monotone normality
zbMATH Keywords: continuous image
zbMATH Keywords: linearly ordered topological space
zbMATH Keywords: compactness
author: Mary Ellen Rudin
reviewed by: K. P. Hart
MaRDI profile type: Publication
cites work: Monotone normality
cites work: Monotonically Normal Spaces
cites work: Q5541832
cites work: Acyclic monotone normality
cites work: Q3027894
cites work: Null-families of subsets of monotonically normal compacta
cites work: Separable zero-dimensional spaces which are continuous images of ordered compacta
cites work: Q3909691
cites work: A Cyclic Monotonically Normal Space which is not K 0
cites work: Monotone normality and compactness
full work available at URL: s0166-8641(97)00068-0
OpenAlex ID: W2093789265
description: scientific article; zbMATH DE number 1121476