Hohti, Aarno On Ginsburg-Isbell derivatives and ranks of metric spaces. (English) Zbl 0558.54020 Pac. J. Math. 111, 39-48 (1984). The author considers metric spaces for which there exists a countable ordinal \(\alpha\) such that the \(\alpha\) th successive Ginsburg-Isbell derivative of the metric uniformity contains every open cover of the space. He shows that a separable metric space has this property if, and only if, it is complete and \(\sigma\)-compact. Reviewer: W.Lindgren Cited in 1 ReviewCited in 3 Documents MSC: 54E35 Metric spaces, metrizability 54E15 Uniform structures and generalizations Keywords:complete \(\sigma \) -compact separable metric space; \(\alpha \) th successive Ginsburg-Isbell derivative; metric uniformity PDFBibTeX XMLCite \textit{A. Hohti}, Pac. J. Math. 111, 39--48 (1984; Zbl 0558.54020) Full Text: DOI