(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}

Definition D519

Set interior

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 $X$ |

Children

▶ | Set exterior |

▶ | Topologically nowhere dense set |

Results

▶ | Every point in open set is an interior point |

▶ | Open set is its own interior |

▶ | Set is a superset to its interior |