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Josia Pietsch 2024-01-24 00:13:59 +01:00
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inputs/lecture_14.tex
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@ -66,7 +66,7 @@
} }
in $(y, <_\Q)$ is in $(y, <_\Q)$ is
cofinal in $(y, <_{\Q})$ and vice versa. cofinal in $(y, <_{\Q})$ and vice versa.
Equivalently, either $(x <^\ast_\phi y)$ Equivalently, either $(x <^\ast_\phi y)$
or or
\begin{IEEEeqnarray*}{rCl} \begin{IEEEeqnarray*}{rCl}
& &x,y \in \WO\\ & &x,y \in \WO\\
@ -84,10 +84,9 @@
such that such that
\[ \[
\forall x \in X.~(\exists n.~(x,n) \in R \iff \exists! n.~(x,n)\in R^\ast). \forall x \in X.~(\exists n.~(x,n) \in R \iff \exists! n.~(x,n)\in R^\ast).
\] \]
We say that $R^\ast$ \vocab[uniformization]{uniformizes} $R$. We say that $R^\ast$ \vocab[uniformization]{uniformizes} $R$.%
\todo{missing picture \footnote{Wikimedia has a \href{https://upload.wikimedia.org/wikipedia/commons/4/4c/Uniformization_ill.png}{nice picture.}}
\url{https://upload.wikimedia.org/wikipedia/commons/4/4c/Uniformization_ill.png}}
\end{theorem} \end{theorem}
\begin{proof} \begin{proof}