Topological Interior

The interior of a subset $S\subseteq X$ of a Topological Space $X$, denoted $\mathrm{int}(S)$, is the union $\bigcup\left\{\;U\in\mathcal{O}({X})\right\}$ of all subsets of $S$ that are open in $X$.

Properties

• The interior forms an Idempotent Comonad on the Power Set of $X$.

• In Classical Mathematics, the interior of $S\subseteq X$ is equal to the Complement of the Exterior of $X$.