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单词 MaximalityPrinciple
释义

maximality principle


Let S be a collectionMathworldPlanetmath of sets. If, for each chain CS, there exists an XS such that every element of C is a subset of X, then S contains a maximal elementMathworldPlanetmath. This is known as the maximality principle.

The maximality principle is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to the axiom of choiceMathworldPlanetmath.

Titlemaximality principle
Canonical nameMaximalityPrinciple
Date of creation2013-03-22 12:26:18
Last modified on2013-03-22 12:26:18
Ownerakrowne (2)
Last modified byakrowne (2)
Numerical id9
Authorakrowne (2)
Entry typeTheorem
Classificationmsc 03E30
Classificationmsc 03E25
Synonymmaximal principle
Related topicZornsLemma
Related topicAxiomOfChoice
Related topicWellOrderingPrinciple
Related topicTukeysLemma
Related topicZermelosPostulate
Related topicHaudorffsMaximumPrinciple
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更新时间:2025/5/5 0:23:43