josia-notes/w23-logic-3
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fixed error
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Josia Pietsch 2024-04-24 13:01:59 +02:00
parent bbb891594c
commit a0cc70cadf
Signed by: josia
GPG Key ID: E70B571D66986A2D
2 changed files with 3 additions and 3 deletions
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2
.gitmodules vendored
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@ -1,3 +1,3 @@
[submodule "LatexPackagesBuild"] [submodule "LatexPackagesBuild"]
path = LatexPackagesBuild path = LatexPackagesBuild
url = https://gitlab.com/latexci/packages/LatexPackagesBuild.git url = https://git.abstractnonsen.se/latex/latex-packages-build

4
inputs/lecture_23.tex
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@ -160,14 +160,14 @@ Let $I$ be a linear order
we have that $F_\gamma = \bigcap_{\alpha < \gamma} F_\alpha$, we have that $F_\gamma = \bigcap_{\alpha < \gamma} F_\alpha$,
since $(X_\gamma,\Z)$ is the inverse limit of since $(X_\gamma,\Z)$ is the inverse limit of
$\{(X_{\alpha}, \Z):\alpha < \gamma\}$. $\{(X_{\alpha}, \Z):\alpha < \gamma\}$.
\item For all $\alpha < \beta$, $F_{\alpha+1} \subsetneq F_\alpha$, \item For all $\alpha$ it is $F_{\alpha+1} \subsetneq F_\alpha$,
because $\pi^{\alpha+1}_\alpha \colon (X_{\alpha+1},\Z) \to (X_\alpha,\Z)$ because $\pi^{\alpha+1}_\alpha \colon (X_{\alpha+1},\Z) \to (X_\alpha,\Z)$
is not a bijection is not a bijection
and all the fibers are isomorphic. and all the fibers are isomorphic.
\end{itemize} \end{itemize}
So $(F_\alpha)_{\alpha \le \beta}$ is a strictly So $(F_\alpha)_{\alpha \le \beta}$ is a strictly
increasing chain of closed subsets. decreasing chain of closed subsets.
But $X$ is second countable, But $X$ is second countable,
so $\beta$ is countable: so $\beta$ is countable:
Let $\{U_n\} = \cB$ be a countable basis Let $\{U_n\} = \cB$ be a countable basis