some small changes
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@ 199,8 +199,8 @@


\[


D \subseteq \N^\N \mathbin{\text{\reflectbox{$\coloneqq$}}} \cN


\]


and a continuous bijection from


$D$ onto $X$ (the inverse does not need to be continuous).


and a continuous bijection $f\colon D \to X$


(the inverse does not need to be continuous).




Moreover there is a continuous surjection $g: \cN \to X$


extending $f$.





@ 64,7 +64,7 @@




Take $S \coloneqq \{s \in \N^{<\N}: \exists x \in D, n \in \N.~x\defon{n} = s\}$.


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\}.


\]




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