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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Topological space

▾ Isolated point

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Topological space

▾ Isolated point

Formulation 0

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}

The

Child definitions