Connectifications of metrizable spaces
type: Item
instance of: scholarly article
title: Connectifications of metrizable spaces
zbMATH Open document ID: 0887.54018
DOI: 10.1016/S0166-8641(97)00067-9
author: Gary Gruenhage
author: John Kulesza
author: Attilio Le Donne
published in: Topology and its Applications
publication date: 1998-05-10T00:00:00Z
review text: \textit{O. T. Alas, M. G. Tkachenko, V. V. Tkachuk} and the reviewer [ibid. 71, No. 3, 203-215 (1996; Zbl 0855.54026)] have shown that every separable metrizable space \(X\) with no compact open sets has a metrizable connectification, that is, there is a connected metrizable space in which \(X\) can be densely embedded; in the same paper, they asked whether the separability condition can be omitted. The first section of the paper under review consists of the construction of a metrizable space with no compact open sets which has no perfectly normal connectification, thus answering negatively the above question. In the second section of the paper, it is shown that every nowhere locally compact metrizable space has a metrizable connectification, thus generalizing a result of \textit{S. Watson} and the reviewer [Houston J. Math. 19, No. 3, 469-481 (1993; Zbl 0837.54012)] who showed that every nowhere locally compact metric space has a Hausdorff connectification.
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1121458
zbMATH Keywords: connectification
zbMATH Keywords: nowhere locally compact metrizable space
reviewed by: Richard G. Wilson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121458