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Josia Pietsch 2024-02-08 15:37:08 +01:00
parent 15c9ff10ea
commit 1d96095f62
Signed by: josia
GPG key ID: E70B571D66986A2D
1 changed files with 4 additions and 4 deletions
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8
inputs/lecture_06.tex
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@ -169,11 +169,11 @@ Furthermore define
i.e.~$\Delta^0_1$ is the set of clopen sets.
\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}
& {\substack{\Sigma_1^0\\\text{open}}} && {\substack{\Sigma^0_2\\F_\sigma}} &&&& {\Sigma^0_\xi} \\
{\substack{\Delta_1^0\\\text{clopen}}} && {\Delta^0_2} && {\Delta^0_3} & \ldots & {\Delta^0_\xi} && {\Delta^0_{\xi + 1}} & \ldots \\
& {\substack{\Pi^0_1\\\text{closed}}} && {\substack{\Pi_2^0\\G_\delta}} &&&& {\Pi^0_\xi}
\arrow["\subseteq", hook, from=2-1, to=1-2]
\arrow["\subseteq"', hook, from=2-1, to=3-2]
\arrow["\subseteq"', hook, from=3-2, to=2-3]