Kuratowski–Zorn lemma (attribution as Zorn’s lemma variant)

E1187537 UNEXPLORED

The Kuratowski–Zorn lemma is a fundamental result in set theory and order theory, equivalent to the Axiom of Choice, which guarantees the existence of maximal elements in certain partially ordered sets.

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All labels observed (3)

Label	Occurrences
Zorn's lemma	7
Kuratowski–Zorn lemma (attribution as Zorn’s lemma variant) canonical	1
Zorns Lemma	1

How this entity was disambiguated

This entity first appeared as the object of triple T15990294 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Kuratowski–Zorn lemma (attribution as Zorn’s lemma variant)
Context triple: [Kazimierz Kuratowski, notableFor, Kuratowski–Zorn lemma (attribution as Zorn’s lemma variant)]

A. Hausdorff maximal principle
The Hausdorff maximal principle is a foundational result in set theory and order theory stating that every partially ordered set contains a maximal totally ordered subset (a maximal chain), and it is equivalent to the axiom of choice.
B. Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
C. Knaster–Kuratowski–Mazurkiewicz lemma
The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
D. Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
E. Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Kuratowski–Zorn lemma (attribution as Zorn’s lemma variant)
Target entity description: The Kuratowski–Zorn lemma is a fundamental result in set theory and order theory, equivalent to the Axiom of Choice, which guarantees the existence of maximal elements in certain partially ordered sets.

A. Hausdorff maximal principle
The Hausdorff maximal principle is a foundational result in set theory and order theory stating that every partially ordered set contains a maximal totally ordered subset (a maximal chain), and it is equivalent to the axiom of choice.
B. Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
C. Knaster–Kuratowski–Mazurkiewicz lemma
The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
D. Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
E. Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
F. None of above. chosen