f: R-R

If f is a one-one mapping, f(K) is compact for every compact set K, then f is continuous?

I guess it is not. right?

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- Oct 23rd 2007, 03:03 PMvioletsfcontinuous and compact
f: R-R

If f is a one-one mapping, f(K) is compact for every compact set K, then f is continuous?

I guess it is not. right? - Oct 23rd 2007, 03:33 PMJhevon
- Oct 23rd 2007, 04:11 PMThePerfectHacker
I think work (it was not so easy to construct a counter example).

f(x) = 1/x for x!=0 and f(x) =0 for x=0.

Can anyone construct a counter-example if f(x) is one-to-one and bounded?