On locally connected connectifications
type: Item
instance of: scholarly article
title: On locally connected connectifications
zbMATH Open document ID: 0928.54018
DOI: 10.1016/S0166-8641(98)00012-1
author: Alessandro Fedeli
author: Attilio Le Donne
published in: Topology and its Applications
publication date: 2000-01-09T00:00:00Z
review text: A connectification of a space \(X\) is a connected topological space \(Y\) containing a dense (homeomorphic) copy of \(X\). The results of the article under review extend theorems of S. Watson and the reviewer [Houston J. Math. 19, No.~3, 469-481 (1993; Zbl 0837.54012))] by showing that each Hausdorff space with a countable \(\pi\)-base and in which regular closed sets are not \(H\)-closed has a locally connected connectification with countable remainder. As an immediate corollary, the Sorgenfrey line has such a connectification, thus answering a question posed by O. T. Alas, M. G. Tkachenko, V. V. Tkachuk and the reviewer (to appear in Commentationes Mathematicae Universitatis Carolinae). Another result implies that each dense-in-itself countable Hausdorff space has a locally connected \(T_2\) connectification.
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54C25
zbMATH DE Number: 1340412
zbMATH Keywords: connectification
zbMATH Keywords: locally connected space
reviewed by: Richard G. Wilson
MaRDI profile type: Publication
Wikidata QID: Q127741068
description: scientific article; zbMATH DE number 1340412