Ordered Locales

Chris Heunen; Nesta van der Schaaf

doi:10.1016/j.jpaa.2024.107654

Ordered Locales

Chris Heunen, Nesta van der Schaaf^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	107654
Pages (from-to)	1-23
Number of pages	23
Journal	Journal of pure and applied algebra
Volume	228
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2024.107654
Publication status	Published - 8 Mar 2024

Keywords / Materials (for Non-textual outputs)

Duality
Locales
Order
Preordered spaces

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title = "Ordered Locales",

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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T1 - Ordered Locales

AU - Heunen, Chris

AU - Schaaf, Nesta van der

PY - 2024/3/8

Y1 - 2024/3/8

N2 - 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.

AB - 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.

KW - Duality

KW - Locales

KW - Order

KW - Preordered spaces

U2 - 10.1016/j.jpaa.2024.107654

DO - 10.1016/j.jpaa.2024.107654

M3 - Article

SN - 0022-4049

VL - 228

SP - 1

EP - 23

JO - Journal of pure and applied algebra

JF - Journal of pure and applied algebra

IS - 7

M1 - 107654

ER -

Ordered Locales

Abstract

Keywords / Materials (for Non-textual outputs)

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