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arXiv · 2303.03813

Ordered Locales

Chris Heunen·Nesta van der Schaaf
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Abstract

We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober $T_0$-ordered spaces with open cones.

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Chris Heunen, Nesta van der Schaaf. 2023-03-07. Ordered Locales. https://doi.org/10.1016/j.jpaa.2024.107654

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