The Stacks project

Definition 26.3.1. Let $f : X \to Y$ be a morphism of locally ringed spaces. We say that $f$ is an open immersion if $f$ is a homeomorphism of $X$ onto an open subset of $Y$, and the map $f^{-1}\mathcal{O}_ Y \to \mathcal{O}_ X$ is an isomorphism.

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View Definition 26.3.1 as pdf