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• W2023370072 abstract "The double powerlocale P(X) (found by composing, in either order, the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Locop,Set] to the double exponential SSX where S is the Sierpiński locale. Further PU(X) and PL(X) are shown to be the subobjects of P(X) comprising, respectively, the meet semilattice and join semilattice homomorphisms. A key lemma shows that, for any locales X and Y, natural transformations from SX (the presheaf Loc(_×X,S)) to SY (i.e. Loc(_×Y,S)) are equivalent to dcpo morphisms (Scott continuous maps) from the frame ΩX to ΩY. It is also shown that SX has a localic reflection in [Locop,Set] whose frame is the Scott topology on ΩX. The reasoning is constructive in the sense of topos validity." @default.
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• W2023370072 date "2004-05-01" @default.
• W2023370072 modified "2023-10-14" @default.
• W2023370072 title "A universal characterization of the double powerlocale" @default.
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• W2023370072 doi "https://doi.org/10.1016/j.tcs.2004.01.034" @default.
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