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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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?
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?
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