Priestley duality for order-preserving maps into distributive lattices |
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Authors: | Jonathan David Farley |
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Affiliation: | (1) Mathematical Institute, University of Oxford, 24-29 St. Giles', OX1 3LB Oxford, United Kingdom;(2) Present address: Mathematical Sciences Research Institute, 1000 Centennial Drive, 94705 Berkeley, CA, USA |
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Abstract: | The category of bounded distributive lattices with order-preserving maps is shown to be dually equivalent to the category of Priestley spaces with Priestley multirelations. The Priestley dual space of the ideal lattice L of a bounded distributive lattice L is described in terms of the dual space of L. A variant of the Nachbin-Stone-ech compactification is developed for bitopological and ordered spaces. Let X be a poset and Y an ordered space; XY denotes the poset of continuous order-preserving maps from Y to X with the discrete topology. The Priestley dual of LP is determined, where P is a poset and L a bounded distributive lattice. |
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Keywords: | 06B10 06A12 06B15 06D05 06E15 18B30 54F05 54E55 54G05 54C10 54C40 54C60 54C20 |
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