some small changes

inputs/lecture_04.tex

@@ -164,4 +164,4 @@ Note that open sets and meager sets have the Baire property.
             by the \yaref{thm:bct}.
     \end{itemize}
 \end{example}
-}
+}{}

inputs/lecture_05.tex

@@ -114,8 +114,8 @@
         \item The intersection of countable many
             open dense sets is dense.
     \end{enumerate}
-    In this case $X$ is called a \vocab{Baire space}.
+    In this case $X$ is called a \vocab{Baire space}.%
-    \footnote{see \yaref{s5e1}}
+    \footnote{cf.~\yaref{s5e1}}
 \end{theoremdef}
 \begin{proof}
     \todo{Proof (short)}
@@ -132,7 +132,6 @@
     This proof can be adapted to other open sets $X$.
 \end{proof}
 
-
 \begin{notation}
     Let $X ,Y$ be topological spaces,
     $A \subseteq  X \times Y$

inputs/lecture_16.tex

@@ -175,9 +175,10 @@ By Zorn's lemma, this will follow from
     \end{IEEEeqnarray*}
 
     The topology induced by the metric
-    is given by basic open subsets\footnote{see Exercise Sheet 9% TODO REF
+    is given by basic open subsets\footnote{cf.~\yaref{s9e2}}
-    }
+    of the form
-    $[U_0; U_1,\ldots, U_n]$, $U_0,\ldots, U_n \overset{\text{open}}{\subseteq} X$,
+    $[U_0; U_1,\ldots, U_n]$,
+    for $U_0,\ldots, U_n \overset{\text{open}}{\subseteq} X$,
     where
     \[
         [U_0; U_1,\ldots,U_n] \coloneqq
@@ -188,8 +189,8 @@ By Zorn's lemma, this will follow from
 We want to view flows as a metric space.
 For a fixed compact metric space $X$,
 we can view the flows $(X,\Z)$ as a subset of $\cC(X,X)$.
-Note that $\cC(X,X)$ is Polish.
+Note that $\cC(X,X)$ is Polish.\footnote{cf.~\yaref{s1e4}}
-Then the minimal flows on $X$ are a Borel subset of $\cC(X,X)$.
+Then the minimal flows on $X$ are a Borel subset of $\cC(X,X)$.\footnote{Exercise} % TODO
 
 However we do not want to consider only flows on a fixed space $X$,
 but we want to look all flows at the same time.