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fixed typos
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Josia Pietsch 2023-12-08 01:42:08 +01:00
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commit c1316d8bb5
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inputs/lecture_15.tex
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@ -91,8 +91,8 @@
Let $X,Y$ be compact metric spaces Let $X,Y$ be compact metric spaces
and $\pi\colon (X,T) \to (Y,T)$ a factor map. and $\pi\colon (X,T) \to (Y,T)$ a factor map.
Then $(X,T)$ is an \vocab{isometric extension} Then $(X,T)$ is an \vocab{isometric extension}
of $(Y,T)$ if there is a real valued $\rho:$ of $(Y,T)$ if there is a real valued $\rho$
defined on the pullback, $\{(x_1,x_2) \in X^2 : \pi(x_1) = \pi(x_2)\}$, % TODO nice notation? defined on $\{(x_1,x_2) \in X^2 : \pi(x_1) = \pi(x_2)\}$
such that such that
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item $\rho$ is continuous. \item $\rho$ is continuous.