ThmDex – An index of mathematical definitions, results, and conjectures.
Every point in open set is an interior point
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $U \in \mathcal{T}$ is an D97: Open set in $T$
Then \begin{equation} U \subseteq \text{int} \langle U \rangle \end{equation}
Proofs
Proof 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $U \in \mathcal{T}$ is an D97: Open set in $T$
This result is a particular case of R4541: Open set is its own interior. $\square$