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Fix typo: Use en dash for separating names: Escardó–Simpson instead of Escardó-Simpson #1185

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mikeshulman merged 1 commit into from
Jul 3, 2025
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Fix typo: Use en dash for separating names: Escardó–Simpson instead of Escardó-Simpson #1185

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6 changes: 3 additions & 3 deletions reals.tex
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Expand Up @@ -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.
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