I'm trying to prove the continuity of the translation map: $f:\mathbb R \to \mathbb R$, defined by $f(x)=x+k$, where $k$ is an integer.
I know that the preimage of an open interval is an open interval. Since an open set of $\mathbb R$ is defined as an union of open intervals, I think the question becomes a little more complex.
Can you help me to prove the continuity of this map?
Thanks