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Math Help - continuous and compact

  1. #1
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    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?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by violetsf View Post
    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?
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  3. #3
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    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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