diff --git a/inputs/lecture_17.tex b/inputs/lecture_17.tex index 5fe9acb..cac776a 100644 --- a/inputs/lecture_17.tex +++ b/inputs/lecture_17.tex @@ -1,5 +1,4 @@ \subsection{The Ellis semigroup} -% TODO ANKI-MARKER \lecture{17}{2023-12-12}{The Ellis semigroup} 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} \begin{subproof} - \todo{Homework} + Cf.~\yaref{s11e1} \end{subproof} 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.} \end{proof} +% TODO ANKI-MARKER + Let $(X,T)$ be a flow. Then by Zorn's lemma, there exists $X_0 \subseteq X$ such that $(X_0, T)$ is minimal.