Stone–Čech compactification

Also known as Čech–Stone compactification, Stone-Cech compactification, Cech-Stone compactification

a universal map from a topological space X to a compact Hausdorff space βX, such that any map from X to a compact Hausdorff space factors through βX uniquely; if X is Tychonoff, then X is a dense subspace of βX