E is closed. - E is complete, i.

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Matreical Daly: analysis
2.4.8. Let X be a complete metric space, and let E be a subset of X. Prove
that the following two statements are equivalent.
(a) E is closed.
(b) E is complete, i.e., every Cauchy sequence of points in E converges to
a point of E.
Transcribed Image Text:2.4.8. Let X be a complete metric space, and let E be a subset of X. Prove that the following two statements are equivalent. (a) E is closed. (b) E is complete, i.e., every Cauchy sequence of points in E converges to a point of E.
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