A morphism of schemes $f: (X,\O_X) \lra (Y,\O_Y)$ is a closed immersion if:

1. As a map of topological spaces, $f: X \lra Y$ is a homeomorphism from $X$ into a closed subset of $Y$ , and
2. the morphism of sheaves $\O_Y \lra \O_X$ associated with $f$ is an epimorphism in the category of sheaves.

This notion is the analog of the notion of closed immersion in the category of differential manifolds.