Re: Prove something about uniformly continuous

"Kenshin" <rurouni_sohjiro@xxxxxxxxxxx> wrote in message
news:1187899369.133388.222390@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
A is nonempty subset of R(eal number)
A : bounded

f : uniformly continuous

f : A -> R

f(A) is bounded?


I wanna prove this by using the definition of uniformly conti
positively...

I've already know the proof making the compact set(the set of limit
points of A).


f(A) need not be bounded, so you should be trying to look for a suitable
counterexample. You say that you know f(A) must be bounded if A is compact,
so for a start, your counterexample cannot have A compact...

Regards,
Mike.




Thank you for your help.



.

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