A finite presentation of the rational Urysohn space
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)].
scientific article; zbMATH DE number 5306962
scientific article