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reference to sheet 11
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Josia Pietsch 2024-02-04 13:38:53 +01:00
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inputs/lecture_17.tex
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@ -1,5 +1,4 @@
\subsection{The Ellis semigroup} \subsection{The Ellis semigroup}
% TODO ANKI-MARKER
\lecture{17}{2023-12-12}{The Ellis semigroup} \lecture{17}{2023-12-12}{The Ellis semigroup}
Let $(X, d)$ be a compact metric space Let $(X, d)$ be a compact metric space
@ -75,7 +74,7 @@ Properties of $(X,T)$ translate to properties of $E(X,T)$:
\] \]
\end{claim} \end{claim}
\begin{subproof} \begin{subproof}
\todo{Homework} Cf.~\yaref{s11e1}
\end{subproof} \end{subproof}
Let $g \in G$. Let $g \in G$.
@ -163,6 +162,8 @@ But it is interesting for other semigroups.
\todo{The other direction is left as an easy exercise.} \todo{The other direction is left as an easy exercise.}
\end{proof} \end{proof}
% TODO ANKI-MARKER
Let $(X,T)$ be a flow. Let $(X,T)$ be a flow.
Then by Zorn's lemma, there exists $X_0 \subseteq X$ Then by Zorn's lemma, there exists $X_0 \subseteq X$
such that $(X_0, T)$ is minimal. such that $(X_0, T)$ is minimal.