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Results tagged with locales
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user 45669
Questions taking place in the category of locales, which is given by the opposite of the category of frames. Also appropriate for questions about pointless topology.
1
vote
Topological regularity for toposes
As far as I am aware, there is not. (Unless, by definition, you want to say that a topos is regular if its localic reflection is regular.)
Not sure if that's helpful!
7
votes
Constructive proofs of existence in analysis using locales
[I don't have enough points to comment; this is just a partial answer, at best]
Steve Vickers' paper https://www.cs.bham.ac.uk/~sjv/CViet.pdf has a constructive version of 1 (IVT). Theorem 41 in Sect …
7
votes
Accepted
Best introductory texts on pointless topology
Topology via Logic - theoretical computer scientist
Stone Spaces - pure mathematician
Both are really good. Topology via logic as it gives a good account of domain theory, including power domains.
…