[Math] Dense sets and Empty Interior

Question

if $A$ is dense in $X$, is there a relation which shows in which cases $A$ has empty interior ? $\mathbb{Q}$ has an empty interior as a dense set in $\mathbb{R}$, so does its complementary in $\mathbb{R}$. The open interval $(a,b)$ is dense in the closure of the same interval but does not have an empty interior. The complementery of $(a,b)$ in its closure consists of the two points $a$ and $b$, which has empty interior. So is there a general statement relating the fact of being dense and having empty interior ?

Thanks for your help.

Answer 1

The complement of a dense set has empty interior.