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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- Mar 9th 2011, 12:36 AMaharonidanContinues 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 - Mar 9th 2011, 01:11 AMFernandoRevilla
- Mar 9th 2011, 01:42 AMaharonidan
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? - Mar 9th 2011, 03:12 AMHallsofIvy
Yes.