inputs/lecture_03.tex

@@ -199,8 +199,8 @@
     \[
         D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN
     \]
-    and a continuous bijection $f\colon D \to X$
-    (the inverse does not need to be continuous).
+    and a continuous bijection from
+    $D$ onto $X$ (the inverse does not need to be continuous).
 
     Moreover there is a continuous surjection $g: \cN \to  X$
     extending $f$.

inputs/lecture_04.tex

@@ -64,7 +64,7 @@
 
     Take $S \coloneqq \{s \in \N^{<\N}: \exists x \in D, n \in \N.~x\defon{n} = s\}$.
     Clearly $S$ is a pruned tree.
-    Moreover, since $D$ is closed, we have that\footnote{cf.~\yaref{s3e1}}
+    Moreover, since $D$ is closed, we have that (cf.~\yaref{s3e1})
     \[
     D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}.
     \]

inputs/lecture_17.tex

@@ -1,4 +1,5 @@
 \subsection{The Ellis semigroup}
+% TODO ANKI-MARKER
 \lecture{17}{2023-12-12}{The Ellis semigroup}
 
 Let $(X, d)$ be a compact metric space
@@ -74,7 +75,7 @@ Properties of $(X,T)$ translate to properties of $E(X,T)$:
         \]
     \end{claim}
     \begin{subproof}
-        Cf.~\yaref{s11e1}
+        \todo{Homework}
     \end{subproof}
 
     Let $g \in G$.
@@ -162,8 +163,6 @@ 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.