some small changes
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@ -199,8 +199,8 @@
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\[
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D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN
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\]
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and a continuous bijection from
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$D$ onto $X$ (the inverse does not need to be continuous).
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and a continuous bijection $f\colon D \to X$
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(the inverse does not need to be continuous).
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Moreover there is a continuous surjection $g: \cN \to X$
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extending $f$.
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@ -64,7 +64,7 @@
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Take $S \coloneqq \{s \in \N^{<\N}: \exists x \in D, n \in \N.~x\defon{n} = s\}$.
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Clearly $S$ is a pruned tree.
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Moreover, since $D$ is closed, we have that (cf.~\yaref{s3e1})
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Moreover, since $D$ is closed, we have that\footnote{cf.~\yaref{s3e1}}
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\[
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D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}.
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\]
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