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[solution] » Let (X,d) be a metric space and (x n ) a sequence. a) Show that

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Let (X,d) be a metric space and (x n ) a sequence. a) Show that
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Let (X,d) be a metric space and (xn) a sequence.

a) Show that if (xn) converges to a point x0, then every subsequence of (xn) also converges to the point x0.

b) Suppose that every subsequence of (xn) has a subsequence converging to a0. Show that also xn --> a as n --> infinity.

 







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