A counterexample in the theory of \(D\)-spaces
type: Item
instance of: scholarly article
title: A counterexample in the theory of \(D\)-spaces
zbMATH Open document ID: 1246.54018
author: Dániel T. Soukup
author: Paul J. Szeptycki
published in: Topology and its Applications
publication date: 2012-06-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.5116
reviewed by: Judith Roitman
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 6049353
zbMATH Keywords: \(D\)-spaces
zbMATH Keywords: Lindelöf spaces
MaRDI profile type: Publication
OpenAlex ID: W2144330606
Wikidata QID: Q124974129
arXiv ID: 1106.5116
cites work: Q3099911
cites work: Q3562023
cites work: Some properties of the Sorgenfrey line and related spaces
cites work: Q3472092
cites work: D-spaces
cites work: Sticks and clubs
cites work: Q3001417
cites work: Some properties of C(X). I
cites work: Set theory. An introduction to independence proofs. 2nd print
cites work: Classes defined by stars and neighbourhood assignments
DOI: 10.1016/J.TOPOL.2012.03.016
review text: ``\(D\)-space'' is a covering property: \(X\) is a \(D\)-space iff, given an open cover \(\{u_x: x \in X\}\) where each \(x \in u_x\), there is a closed discrete subset \(D \subset X\) such that \(\{u_x: x \in D\}\) covers \(X\). Many properties imply \(D\)-space, for example, metrizability. It is not known whether a number of other strong properties imply \(D\)-space, in particular, whether every regular Lindelöf space is a \(D\)-space.NEWLINENEWLINEIn this paper, using a delicate \(\diamondsuit\) construction, the authors show the consistency of the existence of a hereditarily Lindelöf Hausdorff space, all of whose finite powers are Lindelöf, which is not a \(D\)-space.
description: scientific article; zbMATH DE number 6049353