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Notification Bot (Sep 08 2021 at 14:35):Stream created by R Gutin.
R Gutin (Sep 08 2021 at 14:37):I just want to see where to find the rigorous definition of a "space" in computable topology. The work of Paul Taylor and Escardo should provide adequate definitions of "overt", "compact", "Hausdorff" and "discrete" spaces. What seems to be missing is the definition of a space. Thanks.
R Gutin (Sep 08 2021 at 14:43):To be clear, I'd like the unit interval [0,1] over the real line to be compact in this version of Computable Topology. It's likely that in some versions of Computable Topology, this is not the case, but I don't find that to be quite as interesting
Graham Manuell (Sep 08 2021 at 16:42):There are many different approaches to computable topology and each will have a different definition of space. To me one of the more straightforward definitions would be a locale internal to some realisability topos. You can also easily find Paul Taylor's definition in his work on Abstract Stone Duality. Both of these will satisfy your criterion. There are also more spatial approaches which do not.
Matteo Capucci (he/him) (Sep 08 2021 at 20:30):Hi @R Gutin, consider opening a topic in one of the existing streams instead of opening a new one altogether
Notification Bot (Oct 21 2023 at 14:34):Nathanael Arkor changed the access permissions for this stream from Public to Web-public.
Notification Bot (Oct 31 2023 at 11:26):Matteo Capucci (he/him) changed the posting permissions for this stream:
Notification Bot (Oct 31 2023 at 11:26):Matteo Capucci (he/him) renamed stream complete development of computable topology to deprecated: complete development of computable topology.