Stone-Čech extension property
= Stone-Čech extension property
{c}
Every <continuous map> from a space to a <compact Hausdorff space> extends continuously to its <Stone-Čech compactification>. Uniqueness follows from density of the original space and the <Hausdorff> property of the target. Two <Hausdorff compactifications> with this property have comparison maps both ways; their composites fix the <dense> original space and therefore are identity maps, proving equivalence of the compactifications.