On CL-isocompactness and weak Borel completeness
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.
weakly \(\theta \) -refinable spaces of non-measurable cardinality
scientific article; zbMATH DE number 3890326