A finite presentation of the rational Urysohn space
type: Item
instance of: scholarly article
title: A finite presentation of the rational Urysohn space
zbMATH Open document ID: 1196.54049
author: Jan Hubička
author: J. Nešetřil
published in: Topology and its Applications
publication date: 2008-08-06T00:00:00Z
review text: By the Urysohn universal space, the authors mean the space constructed by \textit{P. Urysohn} [Bull. Sci. Math. 51, 43--64, 74--90 (1927; JFM 53.0556.01)] which is a complete, separable metric space which contains an isomorphic copy of every separable metric space. The authors' construction is by finite presentations. The paper also discusses a new finite presentation of posets that are countable, ultrahomogeneous and universal that is different from the authors' finite presentation given in [\textit{J. Hubička} and \textit{J. Nešetřil}, Israel J. Math 149, 21--44 (2008; Zbl 1091.05070)], and relate to their presentation of the Urysohn universal space. They also discuss some of the history of the development of universal spaces. More early history of this topic is given by \textit{M. Hušek} [Topology Appl. 155, No.~14, 1493--1501 (2008; Zbl 1159.54006)].
reviewed by: Jerry E. Vaughan
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54C25
zbMATH DE Number: 5306962
zbMATH Keywords: Urysohn universal space
zbMATH Keywords: complete separable metric spaces
zbMATH Keywords: finite presentations
zbMATH Keywords: generic structures
zbMATH Keywords: concise representations
MaRDI profile type: Publication
full work available at URL: j.topol.2007.06.022
OpenAlex ID: W2055369141
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DOI: 10.1016/J.TOPOL.2007.06.022
description: scientific article; zbMATH DE number 5306962