The Stacks project

Lemma 115.16.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. If there exists a Zariski open covering $X = \bigcup X_ i$ such that each $X_ i$ is very reasonable, then $X$ is very reasonable.

Proof. This is case $(\epsilon )$ of Decent Spaces, Lemma 68.5.2. $\square$

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