Show that if I is bounded, and if f maps every Cauchy sequence in I to a Cauchy sequence, then f is uniformly continuous

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Show that if I is bounded, and if f maps every Cauchy sequence in I to a Cauchy sequence, then f is uniformly continuous

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Show That If I Is Bounded And If F Maps Every Cauchy Sequence In I To A Cauchy Sequence Then F Is Uniformly Continuous 1
Show That If I Is Bounded And If F Maps Every Cauchy Sequence In I To A Cauchy Sequence Then F Is Uniformly Continuous 1 (23.87 KiB) Viewed 92 times
Show that if I is bounded, and if f maps every Cauchy sequence in I to a Cauchy sequence, then f is uniformly continuous. Show by example that the statement fails if the boundedness assumption of I is dropped.
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