Nucleus on a frame
= Nucleus on a frame
{title2=$j:A\to A$}
= Nuclei on a frame
{synonym}
A nucleus is an inflationary, idempotent, finite-meet-preserving map on a <frame>. Its fixed elements form a <frame>, whose joins are obtained by applying $j$ to ambient joins. The induced <locale> is a <sublocale>. The <nuclei on a frame> themselves form a <frame> in pointwise order; their meets are pointwise, but their joins usually are not.