fixed important typo
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Josia Pietsch 2024-02-07 16:04:28 +01:00
parent ffcd9cd45f
commit 82f0dfd4de
Signed by: josia
GPG key ID: E70B571D66986A2D

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@ -179,7 +179,7 @@ since $X^X$ has these properties.
\begin{proof}
Let $G \coloneqq E(X,T)$ and let $d$ be a metric on $X$.
\gist{
For all $g \in G$ we need to show that $x \mapsto gx$ is bijective.
For all $g \in G$ we need to show that $x \mapsto gx$ is injective.
If we had $gx = gy$, then $d(gx,gy) = 0$.
Then $\inf_{t \in T} d(tx,ty) = 0$, but the flow is distal,
hence $x = y$.
@ -195,7 +195,7 @@ since $X^X$ has these properties.
It is $g' = g'gg'$,
so $\forall x .~g'(x) = g'(g g'(x))$.
Hence $g'$ is bijective
Hence $g'$ is injective
and $x = gg'(x)$,
i.e.~$g g' = \id$.
}{