# Math Help - continuous and compact

1. ## continuous 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?

2. Originally Posted by violetsf
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?
Theorem: continuous functions map compact sets to compact sets

does this theorem apply here? can you find a counter-example?

3. 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?