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Lecture 3

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Josia Pietsch 2023-10-17 13:08:17 +02:00
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inputs/lecture_03.tex
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@ -140,7 +140,7 @@
Then let $f(x)$ be the unique point in $X$ Then let $f(x)$ be the unique point in $X$
such that such that
\[ \[
\{f(x)\} = \bigcap_{n} U_{x \defon n} = \bigcap_{n} \overline{U_{x \defon n}. \{f(x)\} = \bigcap_{n} U_{x \defon n} = \bigcap_{n} \overline{U_{x \defon n}}.
\] \]
(This is nonempty as $X$ is a completely metrizable space.) (This is nonempty as $X$ is a completely metrizable space.)
It is clear that $f$ is injective and continuous. It is clear that $f$ is injective and continuous.