# nLab exterior

The exterior of a subset of a topological space is the interior of its complement, or equivalently the complement of its closure. In more elementary terms, $x \in Ext A$ iff there is some neighbourhood of $x$ that is disjoint from $A$.

The exterior operation applied to open sets, i.e., to a topology $\mathcal{O}$ of a space, coincides with the negation operation $\neg: \mathcal{O} \to \mathcal{O}$ when we view $\mathcal{O}$ as a frame or Heyting algebra. See also regular open set.