Dow, Alan; Vermeer, J. An example concerning the property of a space being Lindelöf in another. (English) Zbl 0827.54014 Topology Appl. 51, No. 3, 255-259 (1993). Summary: A space \(X\) is said to be Lindelöf in a space \(Z\) if every open cover of \(Z\) has a countable subcover of \(X\). D. V. Ranchin [Sov. Math., Dokl. 18, 196-200 (1977); translation from Dokl. Akad. Nauk SSSR 232, 1015-1018 (1977; Zbl 0371.54010)] asks if there must always be a Lindelöf \(Y\) with \(X \subset Y \subset Z\). We answer this in the negative. Cited in 1 ReviewCited in 3 Documents MSC: 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) Keywords:Lindelöf in a space Citations:Zbl 0371.54010 PDFBibTeX XMLCite \textit{A. Dow} and \textit{J. Vermeer}, Topology Appl. 51, No. 3, 255--259 (1993; Zbl 0827.54014) Full Text: DOI References: [1] Arhangel’skiǐ, A. V., Some problems and lines of investigations in general topology, Comment. Math. Univ. Carolin., 29, 611-629 (1988) · Zbl 0676.54001 [2] Balcar, B.; Simon, P., Appendix on general topology, (Handbook of Boolean Algebras, Vol. 3 (1989), North-Holland: North-Holland Amsterdam), 1239-1267 [3] Engelking, R., General Topology (1977), PWN: PWN Warsaw [4] Fremlin, D. H., Measure algebras, (Handbook of Boolean Algebras, Vol. 3 (1989), North-Holland: North-Holland Amsterdam), 877-980 [5] Ranchin, D. V., Tightness, sequentiality and closed coverings, Dokl. Akad. Nauk SSSR, 232, 1015-1018 (1977) [6] Solovay, R. M., Real-valued measurable cardinals, (Proceedings of Symposia in Pure Mathematics, 13 (1971), American Mathematical Society: American Mathematical Society Providence, RI), 397-428 · Zbl 0222.02078 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.