# Math Help - Continues functions, Topology

1. ## 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?
sorry if there are spellings mistakes

2. Originally Posted by aharonidan
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.

3. 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?

4. Yes.