Properties (62)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Axiom of Choice
|
| https://www.w3.org/2000/01/rdf-schema#label |
Zorn's Lemma
|
| gptkbp:isA |
Mathematical Principle
|
| gptkbp:isAvenueFor |
Algebra
Topology Functional Analysis |
| gptkbp:isEquippedWith |
Axiom of Choice
|
| gptkbp:isNamedAfter |
gptkb:Max_Zorn
|
| gptkbp:isRelatedTo |
Order Theory
Ordinal Numbers Cardinal Numbers Well-Ordering Theorem Partially Ordered Set Set-Theoretic Foundations Choice Function Maximal Element Theorem Maximal Elements Transfinite_Induction Zorn's_Lemma_in_Abstract_Algebra Zorn's_Lemma_in_Algebra Zorn's_Lemma_in_Algebraic_Geometry Zorn's_Lemma_in_Algebraic_Logic Zorn's_Lemma_in_Algebraic_Structures Zorn's_Lemma_in_Algebraic_Topology Zorn's_Lemma_in_Analysis Zorn's_Lemma_in_Banach_Spaces Zorn's_Lemma_in_Category_Theory Zorn's_Lemma_in_Combinatorics Zorn's_Lemma_in_Commutative_Algebra Zorn's_Lemma_in_Descriptive_Set_Theory Zorn's_Lemma_in_Field_Theory Zorn's_Lemma_in_Functional_Analysis Zorn's_Lemma_in_Functional_Spaces Zorn's_Lemma_in_Galois_Theory Zorn's_Lemma_in_Group_Theory Zorn's_Lemma_in_Hilbert_Spaces Zorn's_Lemma_in_Homological_Algebra Zorn's_Lemma_in_Linear_Algebra Zorn's_Lemma_in_Logic Zorn's_Lemma_in_Measure_Theory Zorn's_Lemma_in_Metric_Spaces Zorn's_Lemma_in_Model_Theory Zorn's_Lemma_in_Noncommutative_Algebra Zorn's_Lemma_in_Number_Theory Zorn's_Lemma_in_Probability_Theory Zorn's_Lemma_in_Representation_Theory Zorn's_Lemma_in_Ring_Theory Zorn's_Lemma_in_Set-Theoretic_Topology Zorn's_Lemma_in_Set_Theory Zorn's_Lemma_in_Topological_Groups Zorn's_Lemma_in_Topological_Spaces Zorn's_Lemma_in_Topology |
| gptkbp:isUsedBy |
Existence of algebraic closures.
Existence of bases in vector spaces. Existence of maximal ideals in rings. |
| gptkbp:isUsedIn |
Combinatorics
Mathematical Logic Set Theory Category Theory Model Theory |
| gptkbp:isVisitedBy |
Axiom of Choice
|
| gptkbp:state |
Every non-empty partially ordered set has at least one maximal element.
|