Properties of Scheme Morphisms
A closed immersion is finite. A finite morphism is proper, affine and of finite type. Finite morphisms are separated. Open immersions are etale, therefore smooth, thus flat; open immersions are separated. Quasi-compact and locally of finite type implies of finite type. Projective and quasi-finite is the same as finite. Proper morphisms are universally closed. Flat morphisms of finite type are universally open.
