Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
The set of isolated points of $E \subseteq X$ in $T$ is the D11: Set \begin{equation} \left\{ x \in E \mid \exists \, U \in \mathcal{T} : U \cap E = \{ x \} \right\} \end{equation}