|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:appliesTo
|
partially ordered sets
|
|
gptkbp:category
|
gptkb:Titan
lemma
|
|
gptkbp:equivalentTo
|
gptkb:Axiom_of_Choice
gptkb:Well-ordering_theorem
|
|
gptkbp:field
|
gptkb:set_theory
|
|
gptkbp:firstPublished
|
1935
|
|
gptkbp:formedBy
|
gptkb:Max_Zorn
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Zorn's lemma
|
|
gptkbp:implies
|
existence of Hamel bases
existence of algebraic closures
existence of maximal ideals
|
|
gptkbp:importantFor
|
foundational in modern mathematics
|
|
gptkbp:language
|
gptkb:German
|
|
gptkbp:namedAfter
|
gptkb:Max_Zorn
|
|
gptkbp:publishedIn
|
gptkb:Mathematische_Zeitschrift
|
|
gptkbp:relatedTo
|
gptkb:Hausdorff_maximal_principle
gptkb:Tychonoff's_theorem
|
|
gptkbp:statedIn
|
Every partially ordered set in which every chain has an upper bound contains at least one maximal element.
|
|
gptkbp:status
|
unprovable in ZF without Axiom of Choice
|
|
gptkbp:usedIn
|
gptkb:algebra
gptkb:topology
gptkb:order_theory
analysis
|
|
gptkbp:bfsParent
|
gptkb:Axiom_of_choice
|
|
gptkbp:bfsLayer
|
5
|