3. Let (X, d) be a metric space. Assume that (Xn) is a sequence in X with a subsequence (Xn;) converging to a E X; that

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3. Let (X, d) be a metric space. Assume that (Xn) is a sequence in X with a subsequence (Xn;) converging to a E X; that

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3 Let X D Be A Metric Space Assume That Xn Is A Sequence In X With A Subsequence Xn Converging To A E X That 1
3 Let X D Be A Metric Space Assume That Xn Is A Sequence In X With A Subsequence Xn Converging To A E X That 1 (63.9 KiB) Viewed 57 times
3. Let (X, d) be a metric space. Assume that (Xn) is a sequence in X with a subsequence (Xn;) converging to a E X; that is, there is a strictly increasing sequence of natural numbers ni < n2 < n3 < such that xn; + a as i +0. Show that if (xn) is Cauchy, then xn + a as n + 0. [Marks: 5]
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