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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.
9
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1
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Is an open map with open relative diagonal necessarily a local homeomorphism?
Let $f : X \to Y$ be an open (and continuous) map of locales. Suppose the relative diagonal $\Delta_f : X \to X \times_Y X$ is an open embedding of locales. … An open embedding of locales is a morphism $f : X \to Y$ that is isomorphic to the inclusion of some open sublocale of $Y$. …
7
votes
1
answer
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Universally closed implies proper for locales
What about locales?
Is there an intuitionistic proof?
It seems to me possible to improve the proof mentioned above, for topological spaces at least. …