From ea31fcac63c76d2a958a6483eb3cc81d08c08a40 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Tue, 21 Nov 2023 13:25:01 +0100
Subject: [PATCH] tutorial

---
 inputs/tutorial_05.tex | 14 +++++++++++++-
 1 file changed, 13 insertions(+), 1 deletion(-)

diff --git a/inputs/tutorial_05.tex b/inputs/tutorial_05.tex
index 6ed47ee..7c9af84 100644
--- a/inputs/tutorial_05.tex
+++ b/inputs/tutorial_05.tex
@@ -18,6 +18,18 @@ and $B_2$ is meager.
      is Baire.
 \end{fact}
 
-\subsection{Exercise 2}
+\subsection{Exercise 4}
+
+\begin{enumerate}[(i)]
+    \item $|B| = \fc$, since $B$ contains a comeager
+        $G_\delta$ set, $B'$:
+        $B'$ is Polish,
+        hence $B' =  P \cup C$
+        for $P$ perfect and $C$ countable,
+        and $|P| \in \{\fc, 0\}$.
+        But $B'$ can't contain isolated point$.
+\end{enumerate}
+
+