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Josia Pietsch 2024-02-08 15:31:30 +01:00
parent af5ccd6c33
commit 15c9ff10ea
Signed by: josia
GPG key ID: E70B571D66986A2D
1 changed files with 15 additions and 17 deletions
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inputs/lecture_06.tex
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@ -168,28 +168,26 @@ Furthermore define
\]
i.e.~$\Delta^0_1$ is the set of clopen sets.
\iffalse % TODO Fix this!
\resizebox{\textwidth}{!}{
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\[\begin{tikzcd}
\adjustbox{width=\textwidth, center}{%
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\begin{tikzcd}
& {\Sigma_1^0} && {\Sigma^0_2} &&&& {\Sigma^0_\xi} \\
{\Delta_1^0} && {\Delta^0_2} && {\Delta^0_3} & \ldots & {\Delta^0_\xi} && {\Delta^0_{\xi + 1}} & \ldots \\
& {\Pi^0_1} && {\Pi_2^0} &&&& {\Pi^0_\xi}
\arrow["\subseteq", hook, from=2-1, to=1-2]
\arrow["\subseteq"', hook', from=2-1, to=3-2]
\arrow[hook, from=3-2, to=2-3]
\arrow[hook, from=1-2, to=2-3]
\arrow[hook, from=2-3, to=1-4]
\arrow[hook', from=2-3, to=3-4]
\arrow[hook, from=2-7, to=1-8]
\arrow[hook', from=2-7, to=3-8]
\arrow[hook, from=1-4, to=2-5]
\arrow[hook', from=3-4, to=2-5]
\arrow[hook, from=1-8, to=2-9]
\arrow[hook', from=3-8, to=2-9]
\end{tikzcd}\]%
\arrow["\subseteq"', hook, from=2-1, to=3-2]
\arrow["\subseteq"', hook, from=3-2, to=2-3]
\arrow["\subseteq", hook, from=1-2, to=2-3]
\arrow["\subseteq", hook, from=2-3, to=1-4]
\arrow["\subseteq"', hook, from=2-3, to=3-4]
\arrow["\subseteq", hook, from=2-7, to=1-8]
\arrow["\subseteq"', hook, from=2-7, to=3-8]
\arrow["\subseteq", hook, from=1-4, to=2-5]
\arrow["\subseteq"', hook, from=3-4, to=2-5]
\arrow["\subseteq", hook, from=1-8, to=2-9]
\arrow["\subseteq"', hook, from=3-8, to=2-9]
\end{tikzcd}%
}
\fi
\begin{proposition}
Let $X$ be a metrizable space.