(i) | $E \subseteq X$ is a D78: Subset of $X$ |

**interior**of $E$ in $T$ is the D11: Set \begin{equation} \text{int}_T \langle E \rangle : = \bigcup \{ U \in \mathcal{T} : U \subseteq E \} \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

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Topological space

Formulation 0

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

The **interior** of $E$ in $T$ is the D11: Set
\begin{equation}
\text{int}_T \langle E \rangle
: = \bigcup \{ U \in \mathcal{T} : U \subseteq E \}
\end{equation}

(i) | $E \subseteq X$ is a D78: Subset of $X$ |

Also known as

Open hull, Generated open set

Child definitions

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