From fc4f57a8b043b95ba7f84a1583333d8ebb0ddd3a Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Fri, 12 Jan 2024 01:44:05 +0100
Subject: [PATCH] small changes
---
inputs/lecture_07.tex | 5 +++--
inputs/lecture_09.tex | 2 +-
2 files changed, 4 insertions(+), 3 deletions(-)
diff --git a/inputs/lecture_07.tex b/inputs/lecture_07.tex
index bae467d..687e009 100644
--- a/inputs/lecture_07.tex
+++ b/inputs/lecture_07.tex
@@ -144,8 +144,9 @@
\begin{proof}
Consider $(F, \cT\defon{F})$ and $(X \setminus F, \cT\defon{X \setminus F})$.
Both are Polish spaces.
- Take the coproduct\footnote{topological sum} $F \oplus (X \setminus F)$
- of these spaces.
+ Take the coproduct%
+ \footnote{In the lecture, this was called the \vocab{topological sum}.}
+ $F \oplus (X \setminus F)$ of these spaces.
This space is Polish,
and the topology is generated by $\cT \cup \{F\}$,
hence we do not get any new Borel sets.
diff --git a/inputs/lecture_09.tex b/inputs/lecture_09.tex
index c3a61ce..ea1c2f6 100644
--- a/inputs/lecture_09.tex
+++ b/inputs/lecture_09.tex
@@ -26,7 +26,7 @@
Let $X$ be a Polish space.
A set $A \subseteq X$
is called \vocab{analytic}
- if
+ iff
\[
\exists Y \text{ Polish}.~\exists B \in \cB(Y).~
\exists \underbrace{f\colon Y \to X}_{\text{continuous}}.~