some small changes

inputs/lecture_03.tex

@@ -199,8 +199,8 @@
     \[
         D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN
     \]
-    and a continuous bijection from
-    $D$ onto $X$ (the inverse does not need to be continuous).
+    and a continuous bijection $f\colon D \to X$
+    (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 (cf.~\yaref{s3e1})
+    Moreover, since $D$ is closed, we have that\footnote{cf.~\yaref{s3e1}}
     \[
     D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}.
     \]