\begin{definition}[Definition:Nowhere Dense/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
$H$ is '''nowhere dense''' in $T$ {{iff}}:
:$\paren {H^-}^\circ = \O$
where $H^-$ denotes the closure of $H$ and $H^\circ$ denotes its interior.
That is, $H$ is '''nowhere dense''' in $T$ {{iff}} the interior of its closure is empty.
Another way of putting it is that $H$ is '''nowhere dense''' in $T$ {{iff}} it consists entirely of boundary.
\end{definition}