Order environments of topological spaces
type: Item
instance of: scholarly article
title: Order environments of topological spaces
zbMATH Open document ID: 1072.54021
author: Klaus Keimel
author: Jihua Liang
publication date: 2005-06-07T00:00:00Z
review text: An order environment of a~space~\(X\) is a~continuous poset~\(D\) such that \(X\) is homeomorphic to the space \(\text{Max}(D)\) of maximal points of~\(D\) with topology inherited from the Scott topology of~\(D\) and such that the Scott topology agree with Lawson topology at \(\text{Max}(D)\). During recent years some classes of spaces (locally compact Hausdorff spaces, complete metric spaces, and Polish spaces) were characterized by means of order environments or domain environments. In the paper under review, the author proves that a~space~\(X\) is Tychonoff if and only if it has a~continuous order environment.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 2174207
zbMATH Keywords: domain environment
zbMATH Keywords: order environment
zbMATH Keywords: weakly complete
zbMATH Keywords: Tikhonov space
MaRDI profile type: Publication
full work available at URL: s10114-004-0365-8
OpenAlex ID: W2023839826
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DOI: 10.1007/S10114-004-0365-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2174207