From 03ebb47099a683d64c5c1a89aba6e8c0fdc1f9fe Mon Sep 17 00:00:00 2001 From: Quirin Schroll Date: Tue, 1 Jul 2025 19:34:41 +0200 Subject: [PATCH] Fix typo of using the wrong dash --- reals.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/reals.tex b/reals.tex index 72b7a8fb..ce09bcb1 100644 --- a/reals.tex +++ b/reals.tex @@ -3035,9 +3035,9 @@ \section{The surreal numbers} \index{Abstract Stone Duality}% This is a (restricted) form of simply typed $\lambda$-calculus with a distinguished object $\Sigma$ which classifies open sets, and by duality also the closed ones. In~\cite{BauerTaylor09} you can also find detailed proofs of the basic properties of arithmetical operations. -The fact that $\RC$ is the least Cauchy complete archimedean ordered field, as was proved in \cref{RC-initial-Cauchy-complete}, indicates that our Cauchy reals probably coincide with the Escard{\'o}-Simpson reals~\cite{EscardoSimpson:01}. -\index{real numbers!Escardo-Simpson@Escard\'o-Simpson}% -It would be interesting to check\index{open!problem} whether this is really the case. The notion of Escard{\'o}-Simpson reals, or more precisely the corresponding closed interval, is interesting because it can be stated in any category with finite products. +The fact that $\RC$ is the least Cauchy complete archimedean ordered field, as was proved in \cref{RC-initial-Cauchy-complete}, indicates that our Cauchy reals probably coincide with the Escard{\'o}--Simpson reals~\cite{EscardoSimpson:01}. +\index{real numbers!Escardo--Simpson@Escard\'o--Simpson}% +It would be interesting to check\index{open!problem} whether this is really the case. The notion of Escard{\'o}--Simpson reals, or more precisely the corresponding closed interval, is interesting because it can be stated in any category with finite products. In constructive set theory augmented by the ``regular extension axiom'', one may also try to define Cauchy completion by closing under limits of Cauchy sequences with a transfinite iteration. It would also be interesting to check whether this construction agrees with ours.