Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Tychonoff_theorem
gptkb:Hamel_basis fields bases ideals modules vector spaces filters rings ultrafilters algebraic closure existence of Hamel bases existence of algebraic bases existence of algebraic closure of fields existence of algebraic closures existence of algebraic extensions existence of algebraic extensions of fields existence of basis in vector spaces existence of linear functionals existence of maximal chains existence of maximal elements in posets existence of maximal filters existence of maximal ideals existence of maximal ideals in commutative rings existence of maximal ideals in rings existence of maximal linearly independent sets existence of maximal subgroups existence of ultrafilters |
| gptkbp:author |
gptkb:Max_Zorn
|
| gptkbp:category |
gptkb:logic
gptkb:order_theory |
| gptkbp:equivalentTo |
gptkb:Axiom_of_Choice
gptkb:Well-ordering_theorem |
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:firstPublished |
1935
|
| https://www.w3.org/2000/01/rdf-schema#label |
Zorn's Lemma
|
| gptkbp:importantFor |
foundational in modern mathematics
|
| gptkbp:language |
English
|
| gptkbp:namedAfter |
gptkb:Max_Zorn
|
| gptkbp:publishedIn |
gptkb:Bulletin_of_the_American_Mathematical_Society
|
| gptkbp:relatedTo |
gptkb:Hausdorff_maximal_principle
transfinite induction |
| gptkbp:sentence |
A partially ordered set in which every chain has an upper bound contains at least one maximal element.
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:topology analysis |
| gptkbp:bfsParent |
gptkb:Tukey's_lemma
gptkb:Axiom_of_Choice |
| gptkbp:bfsLayer |
5
|