Perfect GO-spaces which have a perfect linearly ordered extension
type: Item
instance of: scholarly article
title: Perfect GO-spaces which have a perfect linearly ordered extension
zbMATH Open document ID: 0884.54020
DOI: 10.1016/S0166-8641(97)00019-9
author: Wei-Xue Shi
published in: Topology and its Applications
publication date: 1998-03-17T00:00:00Z
review text: The author considers the old problem of Bennett and Lutzer whether every perfect GO-space can be embedded in a perfect LOTS. In earlier work, in cooperation with \textit{T. Miwa} and \textit{Y.-Z. Gao} [Topology Appl. 66, 241-249 (1995; Zbl 0839.54024)], the author showed that there is an example of a perfect GO-space which cannot be embedded in a perfect LOTS as a dense subspace. A related problem is to characterize the perfect GO-spaces which admit an ``order preserving'' embedding in a perfect LOTS. In the present paper the author presents a characterization of such spaces in terms of the existence of a special \(\sigma\)-discrete subset.
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 1088818
zbMATH Keywords: GO-space
zbMATH Keywords: perfect orderable extension
reviewed by: Jan van Mill
MaRDI profile type: Publication
cites work: On embeddings of perfect GO-spaces into perfect LOTS
cites work: Q3994935
cites work: Q4768329
cites work: On powers of certain lines
cites work: Linearly ordered extensions of GO spaces
cites work: A perfect GO-space which cannot densely embed in any perfect orderable space
cites work: Any perfect GO-space with the underlying LOTS satisfying local perfectness can embed in a perfect LOTS
full work available at URL: s0166-8641(97)00019-9
OpenAlex ID: W2016523178
description: scientific article; zbMATH DE number 1088818