Zorn's Lemma

URI: https://gptkb.org/entity/Zorn%27s_Lemma
GPTKB entity
Statements (63)
Predicate Object
gptkbp:instance_of gptkb:design
gptkbp:applies_to partially ordered sets
gptkbp:has_implications_for existence of maximal elements
https://www.w3.org/2000/01/rdf-schema#label Zorn's Lemma
gptkbp:ingredients gptkb:Max_Zorn
gptkbp:is_a principle of mathematics
gptkbp:is_applied_in abstract algebra
category theory
topological spaces
functional spaces
gptkbp:is_cited_in mathematical literature
gptkbp:is_compared_to Axiom of Choice
gptkbp:is_considered gptkb:constructive_mathematics
mathematical foundations
foundational mathematics
set-theoretic topology
non-standard analysis
gptkbp:is_discussed_in mathematical analysis
mathematical logic
philosophy of mathematics
axiomatic set theory
mathematical proofs
theory of functions
theory of vector spaces
theory of relations
set-theoretic analysis
theory of models
theory of algebraic geometry
theory of categories
theory of sets
theory of cohomology
theory of homology
theory of differential geometry
theory of algebraic structures
theory of algebraic topology
theory of Banach spaces
theory of Hilbert spaces
theory of cardinals
theory of linear spaces
theory of metric spaces
theory of normed spaces
theory of ordinals
theory of topological spaces
gptkbp:is_essential_for certain proofs
gptkbp:is_part_of set-theoretic foundations
gptkbp:is_related_to well-ordering theorem
Zorn's lemma in order theory
chains in partially ordered sets
maximal elements in partially ordered sets
upper bounds in order theory
gptkbp:is_used_in gptkb:topology
gptkb:Mathematics
functional analysis
gptkbp:is_used_to prove the existence of algebraic closures
prove the existence of bases in vector spaces
prove the existence of maximal ideals
gptkbp:named_after gptkb:Max_Zorn
gptkbp:related_to gptkb:Set
order theory
gptkbp:state every chain has an upper bound
gptkbp:used_in gptkb:Mathematics
gptkbp:bfsParent gptkb:The_Axiom_of_Choice
gptkbp:bfsLayer 7