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Josia Pietsch 2023-11-21 13:25:01 +01:00
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@ -18,6 +18,18 @@ and $B_2$ is meager.
is Baire. is Baire.
\end{fact} \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}