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

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

$\mathbb Q$ 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.
• To add, I think $\mathbb{R}\backslash\mathbb{Q}$ is also an example? To generalise, any set $F$ which is dense in $X$, with $X\backslash F$ also dense will have both $F$ and $X\backslash F$ being an appropriate example? – ElfHog Feb 2 '18 at 6:27