How to show that $\exists~f\in C(X,\mathbb R)$ such that $f$ is unbounded?

Asked May 13 '13 at 05:19

Active May 13 '13 at 07:19

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Let $X$ be a non-compact metric space. How to show that $\exists~f\in C(X,\mathbb R)$ such that $f$ is unbounded?

asked May 13 '13 at 05:19

Sriti Mallick

1

if you don't know where to start, thinking about the contradiction may help you see thru some ideas. What is the negation of the conclusion? – Cecile May 13 '13 at 05:33
2

The answer is here. – user10676 May 13 '13 at 07:00

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