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Improve exposition proof of Lemma 0ANV
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aisejohan committed May 5, 2016
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Expand Up @@ -4943,8 +4943,11 @@ \section{Algebras topologically of finite type}
\begin{proof}
Since $X$ and $Y$ are affine it is clear that conditions (1)
and (2) are equivalent. In cases (1) and (2) we see that
$X$ is countably indexed as well by
and (2) are equivalent. In cases (1) and (2) the morphism $f$
is representable by algebraic spaces by definition, hence
affine by Lemma \ref{lemma-affine-representable-by-algebraic-spaces}.
Thus if (1) or (2) holds we see that
$X$ is countably indexed by
Lemma \ref{lemma-property-goes-up-affine-morphism}.
Write $X = \text{Spf}(A)$ and $Y = \text{Spf}(B)$
for topological $S$-algebras $A$ and $B$ in $\textit{WAdm}^{count}$, see
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