Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that

(i)	$E \subseteq X$ is a D78: Subset
(ii)	$\mathcal{I} : = \mathcal{I}_T(E)$ is the D3876: Set of isolated points of $E$ in $T$

Then $E$ is a topologically self-dense in $T$ if and only if \begin{equation} \mathcal{I} = \emptyset \end{equation}