Urysohn universal space, its development and Hausdorff's approach

Miroslav Hušek
2008 Topology and its Applications  
Three approaches to a direct construction of Urysohn universal space are compared, namely those of Urysohn, Hausdorff and Katětov. More details are devoted to the unpublished Hausdorff's approach that is shown to work in a more general situation, too. We shall compare three constructions of Urysohn universal space, namely the original one by Urysohn, an unpublished one by Hausdorff, and finally a general construction given by Katětov. We show that the idea of the Hausdorff's construction works
more » ... or higher cardinals too, like the Katětov's one-the main difference is that the former one gives a concrete description of the space, which may be useful in some situations. We shall not deal with some abstract constructions implying existence of Urysohn universal space like Jónsson classes or Fraïssé limits.
doi:10.1016/j.topol.2008.03.020 fatcat:7vybwl3hrngcxmo64mvzaoyft4