The fundamental duality of partially ordered sets |
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Authors: | B Banaschewski G Bruns |
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Institution: | (1) Department of Mathematics & Statistics, McMaster University, L8S 4KI Hamilton, Ontario, Canada |
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Abstract: | The representation of partially ordered sets by subsets of some set such that specified joins (meets) are taken to unions (intersections) suggests two categories, that of partially ordered sets with specified joins and meets, and that of sets equipped with suitable collections of subsets, and adjoint contravariant functors between them. This, in turn, induces a duality including, among several others, the two Stone Dualities and that between spatial locales and sober spaces. |
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Keywords: | 06A99 18B99 |
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