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Math Help - Continues functions, Topology

  1. #1
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    Continues functions, Topology

    a. what are all the continues functions from R to Z according to the standard metric on R?
    b. same question about R to Z^2?
    thanks for your help
    sorry if there are spellings mistakes
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by aharonidan View Post
    a. what are all the continues functions from R to Z according to the standard metric on R?

    Hint : \mathbb{R} is connected so, f assumes as a value each number between any two of its values.
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  3. #3
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    Thanks for the hint... got it.
    Z is a discrete space thus the open sets in Z are the singltons, therefore only constant are continues. am I correct?
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    Yes.
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