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Pseudoideal : ウィキペディア英語版
Pseudoideal
In the theory of partially ordered sets, a pseudoideal is a subset characterized by a bounding operator LU.
== Basic definitions ==
LU(''A'') is the set of all lower bounds of the set of all upper bounds of the subset ''A'' of a partially ordered set.
A subset ''I'' of a partially ordered set (''P'',≤) is a Doyle pseudoideal, if the following condition holds:
For every finite subset ''S'' of ''P'' that has a supremum in ''P'', ''S''\subseteq ''I'' implies that LU(''S'') \subseteq ''I''.
A subset ''I'' of a partially ordered set (''P'',≤) is a pseudoideal, if the following condition holds:
For every subset ''S'' of ''P'' having at most two elements that has a supremum in ''P'', ''S''\subseteq ''I'' implies that LU(''S'') \subseteq ''I''.

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