Many for the price of one duality principle for affine sets (Q748704)
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scientific article; zbMATH DE number 6502195
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Many for the price of one duality principle for affine sets |
scientific article; zbMATH DE number 6502195 |
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Many for the price of one duality principle for affine sets (English)
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29 October 2015
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By considering topological spaces as generalised orders, \textit{D. Hofmann} [Order 30, No. 2, 643--655 (2013; Zbl 1282.54010)] has shown that the category of distributive spaces is dually equivalent to a certain category of frames. The aim of this paper is to extend the machinery of D. Hofmann to the setting of affine sets by considering affine sets as a generalization of topological spaces. It is shown that the result of D. Hofmann motivates many dualities of the similar kind under certain assumptions.
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affine set
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filter monad
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frame
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limit point of a filter
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sobriety
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spatiality
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