\begin{definition}[Definition:Everywhere Dense/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a subset.
The subset $H$ is '''(everywhere) dense in $T$''' {{iff}}:
:$H^- = S$
where $H^-$ is the closure of $H$.
That is, {{iff}} every point in $S$ is a point or a limit point of $H$.
\end{definition}