▾ 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
Set interior
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $E \subseteq X$ is a D78: Subset of $X$
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}
Also known as
Open hull, Generated open set
Child definitions
» D520: Set exterior
» D246: Topologically nowhere dense set
Results
» R1149: Every point in open set is an interior point
» R4541: Open set is its own interior
» R3945: Set is a superset to its interior