Thread: 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

Originally Posted by aharonidan

a. what are all the continues functions from R to Z according to the standard metric on R?

Hint : is connected so, 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.