nLab
open immersion of schemes

A morphism f:XY of schemes is an open immersion if the underlying morphism of topological spaces is a homeomorphism onto an open image and the comorphism f :𝒪 Yf *𝒪 X is an isomorphism of sheaves when restricted to the image of f. In other words, an open immersion is a morphism of schemes which decomposes uniquely into an isomorphism of schemes and the identity inclusion of an open subscheme.