Nowhere dense set

A nowhere dense set in a topological space $X$ is a subset $A\subseteq X$ such that the interior of its closure is empty , i.e. $\operatorname{int}(\overline{A})=\varnothing$.

Equivalently, $A$ is nowhere dense if $\overline{A}$ contains no nonempty open set . Nowhere dense sets are the basic building blocks of meager sets in the Baire category viewpoint.

Examples:

• The set of integers $\mathbb{Z}\subseteq \mathbb{R}$ (with the usual topology) is nowhere dense: it is closed and has empty interior.
• The set $\{1/n : n\in\mathbb{N}\}\subseteq \mathbb{R}$ is nowhere dense: its closure is $\{1/n:n\in\mathbb{N}\}\cup\{0\}$, which has empty interior.