In particular, projective spaces satisfy a condition called properness which is analogous to compactness. Properties that descend include flatness, smoothness, properness, and many other classes of morphisms. This is useful for building intuition with the Valuative criterion of properness. The same goes for properness and many other properties. It is commonly called the valuative criterion of properness. There is a very intuitive criterion for properness which goes back to Chevalley.