Definition:Nowhere Dense/Definition 1

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$.

$H$ is nowhere dense in $T$ :
 * $\paren {H^-}^\circ = \O$

where $H^-$ denotes the closure of $H$ and $H^\circ$ denotes its interior.

That is, $H$ is nowhere dense in $T$ the interior of its closure is empty.

Another way of putting it is that $H$ is nowhere dense in $T$ it consists entirely of boundary.

Also see

 * Equivalence of Definitions of Nowhere Dense