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Fix equivalence relation defining the stalk
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aisejohan committed Sep 2, 2013
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8 changes: 4 additions & 4 deletions sheaves.tex
Expand Up @@ -923,10 +923,10 @@ \section{Stalks}
x\in U, s\in \mathcal{F}(U)
\}/\sim
$$
with equivalence relation given by $(U, s) \sim (U', s')$
if and only if $s|_{U\cap U'} = s'|_{U\cap U'}$. By abuse of
notation we will often denote $(U, s)$, $s_x$,
or even $s$ the corresponding element in $\mathcal{F}_x$.
with equivalence relation given by $(U, s) \sim (U', s')$ if and only if
there exists an open $U'' \subset U \cap U'$ with $x \in U''$ and
$s|_{U''} = s'|_{U''}$. By abuse of notation we will often denote
$(U, s)$, $s_x$, or even $s$ the corresponding element in $\mathcal{F}_x$.
Also we will say $s = s'$ in $\mathcal{F}_x$ for two local sections
of $\mathcal{F}$ defined in an open neighbourhood of $x$ to denote that
they have the same image in $\mathcal{F}_x$.
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