Lemma 87.16.1. Let $S$ be a scheme. Let $X$ be a formal algebraic space over $S$. The following are equivalent

the reduction of $X$ (Lemma 87.12.1) is a quasi-separated algebraic space,

for $U \to X$, $V \to X$ with $U$, $V$ quasi-compact schemes the fibre product $U \times _ X V$ is quasi-compact,

for $U \to X$, $V \to X$ with $U$, $V$ affine the fibre product $U \times _ X V$ is quasi-compact.

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