Statements (68)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:physicist
|
| gptkbp:bfsLayer |
6
|
| gptkbp:bfsParent |
gptkb:Steinhaus–_Borsuk–_Lebesgue–_Kuratowski–_Zorn_theorem
gptkb:Steinhaus–_Borsuk–_Lebesgue–_Zorn_theorem |
| gptkbp:applies_to |
order theory
partially ordered sets |
| https://www.w3.org/2000/01/rdf-schema#label |
Zorn's lemma
|
| gptkbp:is_a |
principle of maximality
|
| gptkbp:is_cited_in |
gptkb:Research_Institute
|
| gptkbp:is_compared_to |
the Axiom of Choice
|
| gptkbp:is_considered |
mathematical logic
|
| gptkbp:is_described_as |
mathematical textbooks
|
| gptkbp:is_discussed_in |
set theory literature
|
| gptkbp:is_fundamental_to |
modern mathematics
|
| gptkbp:is_related_to |
abstract algebra
algebraic topology category theory topological spaces cardinal numbers continuum hypothesis mathematical foundations axiomatic set theory functional spaces mathematical proofs ordinal numbers combinatorial set theory algebraic structures mathematical induction maximal ideals well-ordering theorem order types set-theoretic topology transfinite induction axioms of set theory well-ordered sets theory of algebraic structures theory of cardinals theory of ordinals theory of topological spaces closure operators Zorn's lemma and choice principles chain condition finite and infinite sets functional analysis concepts lattices maximal chains maximal elements in posets maximal filters theory of chains theory of closure operators theory of filters theory of ideals theory of lattices theory of maximal elements |
| gptkbp:is_tested_for |
Zorn's lemma proof techniques
|
| gptkbp:is_used_in |
gptkb:Mathematician
gptkb:television_channel functional analysis |
| gptkbp:is_used_to |
prove the existence of algebraic closures
prove the existence of bases in vector spaces prove the existence of certain types of filters prove the existence of maximal ideals in rings prove the existence of ultrafilters prove the existence of maximal elements in various structures |
| gptkbp:named_after |
gptkb:Max_Zorn
|
| gptkbp:related_to |
gptkb:collection
|
| gptkbp:state |
every non-empty partially ordered set has at least one maximal element
|
| gptkbp:used_in |
gptkb:Mathematician
|