Assume that the metric space $(X, d)$ is not compact then there exist a $f: X \to \Bbb R$ which is continuous but not bounded.

Asked Feb 17 '15 at 15:52

Active Feb 18 '15 at 09:13

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Assume that the metric space $(X, d)$ is not compact then there exist a $f: X \to \Bbb R$ which is continuous but not bounded.

I am finding difficulty in constructing such a function!!

asked Feb 17 '15 at 15:52

User8976

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See the answers here. – David Mitra Feb 17 '15 at 15:58
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other examples can be interesting to see. – Seyhmus Güngören Feb 17 '15 at 16:13

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