Ultrafilter limit map for a dense continuous image
= Ultrafilter limit map for a dense continuous image
{title2=$\Lambda(\mathcal H)=\lim f_*\mathcal H$}
A <continuous> <dense> map into a <compact> <Hausdorff space> assigns to each <ultrafilter> on its domain the unique limit of its pushforward. This limit map is <surjective> by the <ultrafilter> characterization of image <closure>. It is <injective> exactly when disjoint domain <subsets> have disjoint image <closures>.