closed immersion

A morphism of schemes $f:(X,\\mathcal{O}_{X})\\longrightarrow(Y,\\mathcal{O}_{Y})$ is a closed immersion if:

1.
As a map of topological spaces, $f:X\\longrightarrow Y$ is a homeomorphism from $X$ into a closed subset of $Y$ , and
2.
the morphism of sheaves $\\mathcal{O}_{Y}\\longrightarrow\\mathcal{O}_{X}$ associated with $f$ is an epimorphism (http://planetmath.org/AbelianCategory) in the category of sheaves.

This notion is the analog of the notion of closed immersion (http://planetmath.org/Immersion) in the category of differential manifolds.

单词	ClosedImmersion
释义	closed immersion A morphism of schemes $f:(X,\\mathcal{O}_{X})\\longrightarrow(Y,\\mathcal{O}_{Y})$ is a closed immersion if: 1. As a map of topological spaces, $f:X\\longrightarrow Y$ is a homeomorphism from $X$ into a closed subset of $Y$ , and 2. the morphism of sheaves $\\mathcal{O}_{Y}\\longrightarrow\\mathcal{O}_{X}$ associated with $f$ is an epimorphism (http://planetmath.org/AbelianCategory) in the category of sheaves. This notion is the analog of the notion of closed immersion (http://planetmath.org/Immersion) in the category of differential manifolds.
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