From 37f81861dfadd0610b784f40395943a20c30345a Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Fri, 2 Feb 2024 01:59:54 +0100
Subject: [PATCH] some small changes

---
 inputs/lecture_15.tex  |  5 ++---
 inputs/lecture_16.tex  |  1 +
 inputs/tutorial_14.tex |  2 +-
 inputs/tutorial_15.tex | 10 ++++------
 4 files changed, 8 insertions(+), 10 deletions(-)

diff --git a/inputs/lecture_15.tex b/inputs/lecture_15.tex
index 4550520..53092a8 100644
--- a/inputs/lecture_15.tex
+++ b/inputs/lecture_15.tex
@@ -254,15 +254,14 @@ Recall:
     Hence $x_1 = x_2$ $\lightning$.
 \end{proof}
 
-% TODO ANKI-MARKER
 \begin{definition}
     Let $\Sigma = \{(X_i, T) : i \in I\} $
     be a collection of factors of $(X,T)$.
     Let $\pi_i\colon (X,T) \to (X_i, T)$ denote the factor map.
     Then $(X, T)$ is a \vocab{limit}%
     \footnote{This is not a limit in the category theory sense and not uniquely determined.}
-    of $\Sigma$
-    iff
+    % TODO THE inverse limit is A limit
+    of $\Sigma$ iff
     \[
     \forall x_1,x_2 \in X.~\exists i \in I.~\pi_i(x_1) \neq \pi_i(x_2).
     \]
diff --git a/inputs/lecture_16.tex b/inputs/lecture_16.tex
index adf914f..c0a5161 100644
--- a/inputs/lecture_16.tex
+++ b/inputs/lecture_16.tex
@@ -1,4 +1,5 @@
 \lecture{16}{2023-12-08}{}
+% TODO ANKI-MARKER
 
 $X$ is always compact metrizable.
 
diff --git a/inputs/tutorial_14.tex b/inputs/tutorial_14.tex
index f4f9f41..77c2478 100644
--- a/inputs/tutorial_14.tex
+++ b/inputs/tutorial_14.tex
@@ -23,7 +23,7 @@
         such that for all $t \in T$, $d(ta,tb) > \epsilon$.
 
 
-    \item % TODO (not too hard)
+    \item \todo{TODO}% TODO (not too hard)
         % (b)
         % Let $(X,T)$ be distal with a dense orbit,
         % then it is distal minimal.
diff --git a/inputs/tutorial_15.tex b/inputs/tutorial_15.tex
index 9bb251a..2da6ab1 100644
--- a/inputs/tutorial_15.tex
+++ b/inputs/tutorial_15.tex
@@ -1,12 +1,11 @@
-\tutorial{15}{2024-01-31}{Additions}
-
 \subsection{Additional Tutorial}
+\tutorial{15}{2024-01-31}{Additions}
 
 The following is not relevant for the exam,
 but gives a more general picture.
 
-Let $ X$ be a topological space.
-Let $\cF$ be a filter on $ X$.
+Let $X$ be a topological space
+and let $\cF$ be a filter on $ X$.
 
 $x \in X$ is a limit point of $\cF$ iff the neighbourhood filter $\cN_x$,
 all sets containing an open neighbourhood of $x$,
@@ -83,5 +82,4 @@ Consider the basic open set
 \{\cF \in  \beta\N  : \cF \ni f^{-1}(V)\}.
 \]
 
-
-
+% TODO