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some small changes

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Josia Pietsch 2024-02-04 01:36:10 +01:00
parent 24ed36d0a7
commit 236874b1a5
Signed by: josia
GPG key ID: E70B571D66986A2D
2 changed files with 3 additions and 3 deletions
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4
inputs/lecture_03.tex
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@ -199,8 +199,8 @@
\[ \[
D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN
\] \]
and a continuous bijection from and a continuous bijection $f\colon D \to X$
$D$ onto $X$ (the inverse does not need to be continuous). (the inverse does not need to be continuous).
Moreover there is a continuous surjection $g: \cN \to X$ Moreover there is a continuous surjection $g: \cN \to X$
extending $f$. extending $f$.

2
inputs/lecture_04.tex
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@ -64,7 +64,7 @@
Take $S \coloneqq \{s \in \N^{<\N}: \exists x \in D, n \in \N.~x\defon{n} = s\}$. Take $S \coloneqq \{s \in \N^{<\N}: \exists x \in D, n \in \N.~x\defon{n} = s\}$.
Clearly $S$ is a pruned tree. Clearly $S$ is a pruned tree.
Moreover, since $D$ is closed, we have that (cf.~\yaref{s3e1}) Moreover, since $D$ is closed, we have that\footnote{cf.~\yaref{s3e1}}
\[ \[
D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}. D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}.
\] \]