×

Paracompactness in locally Lindelöf spaces. (English) Zbl 0599.54027

We quote the main results of this interesting paper: (1) a regular, locally Lindelöf, submetalindelöf space is paracompact if and only if it is strongly collectionwise Hausdorff. (2) Assuming \(2^{\omega_ 1}>2^{\omega}\), every connected, normal, locally Lindelöf, submetalindelöf space of countable tightness and character \(\leq 2^{\omega}\) is paracompact. In particular, \(2^{\omega_ 1}>2^{\omega}\) implies that every connected, locally Lindelöf, normal Moore space is metrizable. (3) Assuming \(2^{\omega_ 1}>2^{\omega}\), every connected, normal, locally compact, submetalindelöf space is paracompact. Using Theorem (1), two questions raised by F. D. Tall, respectively S. Watson, are answered.
Reviewer: H.Brandenburg

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E30 Moore spaces
54D45 Local compactness, \(\sigma\)-compactness
54A35 Consistency and independence results in general topology
PDFBibTeX XMLCite
Full Text: DOI