From 236874b1a54d02eb85ed060f14ddb5c836594af5 Mon Sep 17 00:00:00 2001 From: Josia Pietsch Date: Sun, 4 Feb 2024 01:36:10 +0100 Subject: [PATCH] some small changes --- inputs/lecture_03.tex | 4 ++-- inputs/lecture_04.tex | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/inputs/lecture_03.tex b/inputs/lecture_03.tex index 85c8c5a..55be7af 100644 --- a/inputs/lecture_03.tex +++ b/inputs/lecture_03.tex @@ -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 $f$. diff --git a/inputs/lecture_04.tex b/inputs/lecture_04.tex index 8267a0f..4b7ff7a 100644 --- a/inputs/lecture_04.tex +++ b/inputs/lecture_04.tex @@ -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}} \[ D = [S] = \{x \in \N^\N : \forall n \in \N.~x\defon{n} \in S\}. \]