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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Originally Posted by aharonidan a. what are all the continues functions from R to Z according to the standard metric on R? Hint : $\displaystyle \mathbb{R}$ is connected so, $\displaystyle f$ assumes as a value each number between any two of its values.
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?
Yes.
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