From 72025f8ea82a77e6ec23ee662639aa8f499972a4 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Fri, 12 Jan 2024 01:31:12 +0100
Subject: [PATCH] clopenization

---
 inputs/lecture_07.tex | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/inputs/lecture_07.tex b/inputs/lecture_07.tex
index 169fc76..bae467d 100644
--- a/inputs/lecture_07.tex
+++ b/inputs/lecture_07.tex
@@ -77,11 +77,18 @@
 
 \subsection{Turning Borels Sets into Clopens}
 
-\begin{theorem}
+\begin{theorem}%
+    \footnote{Whilst strikingly concise the verb ``\vocab[Clopenization™]{to clopenize}''
+            unfortunately seems to be non-standard vocabulary.
+            Our tutor repeatedly advised against using it in the final exam.
+            Contrary to popular belief
+            the very same tutor was \textit{not} the one first to introduce it,
+            as it would certainly be spelled ``to clopenise'' if that were the case.
+        }
     \label{thm:clopenize}
     Let $(X, \cT)$ be a Polish space.
     For any  Borel set $A \subseteq  X$,
-    there is a finer Polish topology,
+    there is a finer Polish topology,%
     \footnote{i.e.~$\cT_A \supseteq \cT$ and $(X, \cT_A)$ is Polish}
     such that
     \begin{itemize}