Abstract
Any subset of a metric space is itself a metric space, with the same distance function. It is obvious that any closed subset of a complete metric space is complete with respect to the same metric. When can a subspace be remetrized so as to be complete? This question is answered by the following
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© 1980 Springer-Verlag New York Inc.
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Oxtoby, J.C. (1980). The Theorem of Alexandroff. In: Measure and Category. Graduate Texts in Mathematics, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9339-9_12
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DOI: https://doi.org/10.1007/978-1-4684-9339-9_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9341-2
Online ISBN: 978-1-4684-9339-9
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