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, xExtAx \in Ext A iff there is some neighbourhood of xx that is disjoint from AA.

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

Last revised on September 17, 2018 at 10:27:56. See the history of this page for a list of all contributions to it.