Closed nucleus
= Closed nucleus
{title2=$c(a)(x)=a\vee x$}
This <nucleus on a frame> determines the <closed sublocale> complementary to the open determined by $a$. It is the least <nucleus on a frame> taking $0$ to $a$. In the <frame> of <nuclei on a frame>, $c(a)$ and the <open nucleus> $o(a)$ are complements.