Lemma 109.74.2. There exists an affine formal algebraic space $X$ whose regular functions do not separate points, in the following sense: If we write $X = \mathop{\mathrm{colim}}\nolimits X_\lambda$ as in Formal Spaces, Definition 86.9.1 then $\mathop{\mathrm{lim}}\nolimits \Gamma (X_\lambda , \mathcal{O}_{X_\lambda })$ is a field, but $X_{red}$ has infinitely many points.

Proof. See discussion above. $\square$

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