is there a set exists with no interior and no isolated point?

Question

Is there exists any subset of real number with no interior and no isolated point ?
I know the basic definitions of both of them.I thinks that set of rational number could be one ?
But i m not sure
Any help would be appreciated

Answer 1

$\mathbb Q$ is appropriate. It has no interior since $\mathbb R$ \ $\mathbb Q$ is dense, and it has no isolated point since it is dense itself.

$\emptyset$ too.