×

A solution of Matveev’s question. (English) Zbl 1009.54028

Summary: A space \(X\) is discretely absolutely star-Lindelöf if for every open cover \({\mathcal U}\) of \(X\) and every dense subset \(D\) of \(X\), there exists a countable subset \(F\subseteq D\) such that \(F\) is discrete closed in \(X\) and \(St(F,{\mathcal U})=X\). We construct an example of a normal discretely absolutely star-Lindelöf space with an uncountable discrete closed subspace under \(2^{\aleph_0} =2^{\aleph_1}\) which gives a partial answer to a question of M. V. Matveev.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10 Product spaces in general topology
54D55 Sequential spaces
PDF BibTeX XML Cite