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On Ginsburg-Isbell derivatives and ranks of metric spaces. (English) Zbl 0558.54020

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

MSC:

54E35 Metric spaces, metrizability
54E15 Uniform structures and generalizations
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