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Remove "X is Sober and"
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aisejohan committed Jul 20, 2021
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Expand Up @@ -107,6 +107,7 @@ Jonas Ehrhard
Alexander Palen Ellis
Matthew Emerton
Aras Ergus
Tim Evink
Andrew Fanoe
Maxim Fedorchuck
Hu Fei
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2 changes: 1 addition & 1 deletion topology.tex
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Expand Up @@ -4131,7 +4131,7 @@ \section{Spectral spaces}
we see that $\bigcap (U_i \cap E)$ is nonempty by
Lemma \ref{lemma-constructible-hausdorff-quasi-compact} and
Lemma \ref{lemma-intersection-closed-in-quasi-compact}.
Since $X$ is a sober space and $\{U_i\}$ is a
Since $\{U_i\}$ is a
fundamental system of open neighbourhoods of $x$, we see that
$\bigcap U_i$ is the set of generalizations of $x$. Thus
$x$ is a specialization of a point of $E$.
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