On CL-isocompactness and weak Borel completeness
type: Item
instance of: scholarly article
title: On CL-isocompactness and weak Borel completeness
zbMATH Open document ID: 0558.54015
author: Masami Sakai
published in: Tsukuba Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The author defines a Tychonoff space to be CL-isocompact if the closure of each of its countably compact subspaces is compact, and derives a number of elementary properties of CL-isocompactness, the majority of which are special cases of 3.6 of the reviewer's paper [Trans. Am. Math. Soc. 210, 365-385 (1975; Zbl 0335.54020)]. A Tychonoff space is weakly Borel complete if each Borel ultrafilter \({\mathcal B}\) on X with c.i.p. has the property that the intersection of the zero-sets of X in \({\mathcal B}\) is non-empty. The author shows: (1) weakly Borel complete spaces are CL- isocompact, and (2) weakly \(\theta\)-refinable spaces of non-measurable cardinality are weakly Borel complete. Some corollaries of these results are derived.
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 3890326
zbMATH Keywords: CL-isocompact Tikhonov spaces
zbMATH Keywords: Borel ultrafilter
zbMATH Keywords: weakly Borel complete spaces
zbMATH Keywords: weakly \(\theta \) -refinable spaces of non-measurable cardinality
reviewed by: R. G. Woods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160049
OpenAlex ID: W2235236885
DOI: 10.21099/TKBJM/1496160049
description: scientific article; zbMATH DE number 3890326