The Stacks project

Lemma 65.12.2. Let $S \in \mathop{\mathrm{Ob}}\nolimits (\mathit{Sch}_{fppf})$ be a scheme. A composition of (closed, resp. open) immersions of algebraic spaces over $S$ is a (closed, resp. open) immersion of algebraic spaces over $S$.

Proof. See Lemma 65.5.4 and Remarks 65.4.3 (see very last line of that remark) and 65.4.2. $\square$

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