Skip to content

Commit 3afc33d

Browse files
authored
Merge pull request #1185 from Bolpat/patch-5
Fix typo: Use en dash for separating names: Escardó–Simpson instead of Escardó-Simpson
2 parents ffeb7cd + 03ebb47 commit 3afc33d

File tree

1 file changed

+3
-3
lines changed

1 file changed

+3
-3
lines changed

reals.tex

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -3035,9 +3035,9 @@ \section{The surreal numbers}
30353035
\index{Abstract Stone Duality}%
30363036
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.
30373037

3038-
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}.
3039-
\index{real numbers!Escardo-Simpson@Escard\'o-Simpson}%
3040-
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.
3038+
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}.
3039+
\index{real numbers!Escardo--Simpson@Escard\'o--Simpson}%
3040+
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.
30413041

30423042
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.
30433043
It would also be interesting to check whether this construction agrees with ours.

0 commit comments

Comments
 (0)