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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.
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Locales as spaces of ideal/imaginary points
Yes, there is a general theory of locales as spaces of imaginary points. … The theory of classifying locales indeed allows you to construct spaces (locales) of things which aren't expected to exist, just by writing down the axioms of the hypothetical objects. …