Arhangel’skii, A. V.; Yaschenko, I. V. Relatively compact spaces and separation properties. (English) Zbl 0851.54024 Commentat. Math. Univ. Carol. 37, No. 2, 343-348 (1996). Call a subset \(A\) of a space \(X\) relatively compact if every open cover of \(X\) has a finite subfamily that covers \(A\). A space is potentially compact if it can be embedded in some other space as a relatively compact subset. The authors note that, among Hausdorff spaces, complete regularity implies potential compactness which in turn implies regularity. Using various inputs to Jones’ machine [F. B. Jones, Lect. Notes Math. 375, 149-152 (1974; Zbl 0286.54008)] they provide examples to show that neither implication can be reversed. The paper closes with two questions; one asks for an internal characterization of potential compactness, the other asks for a regular space without a dense completely regular subspace. Reviewer: K.P.Hart (Delft) Cited in 3 Documents MSC: 54D30 Compactness 54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.) 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) Keywords:relative compactness; complete regularity Citations:Zbl 0286.54008 PDFBibTeX XMLCite \textit{A. V. Arhangel'skii} and \textit{I. V. Yaschenko}, Commentat. Math. Univ. Carol. 37, No. 2, 343--348 (1996; Zbl 0851.54024) Full Text: EuDML