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  3. 18.2.14. problem. give examples of metric spaces m

18.2.14. Problem. Give examples of metric spaces M and N , a homeomorphism f : M...

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Advance Math

18.2.14. Problem. Give examples of metric spaces M and N , ahomeomorphism f : M ? N , and
a Cauchy sequence (xn) in M such that the sequence ?f(xn)? isnot Cauchy in N.
18.2.15. Problem. Show that if D is a dense subset of a metricspace M and every Cauchy
sequence in D converges to a point of M, then M iscomplete.

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