Connectifications of metrizable spaces
\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.
nowhere locally compact metrizable space
scientific article; zbMATH DE number 1121458
scientific article