ThmDex – An index of mathematical definitions, results, and conjectures.
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
Definition D519
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}
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