Triple

T21046779
Position Surface form Disambiguated ID Type / Status
Subject Knaster–Kuratowski–Mazurkiewicz lemma E518469 entity
Predicate relatedTo P37 FINISHED
Object Borsuk–Ulam theorem NE NERFINISHED

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Borsuk–Ulam theorem
Context triple: [Knaster–Kuratowski–Mazurkiewicz lemma, relatedTo, Borsuk–Ulam theorem]
  • A. Borsuk–Ulam theorem chosen
    The Borsuk–Ulam theorem is a fundamental result in algebraic topology stating that any continuous map from an n-dimensional sphere to Euclidean n-space maps some pair of antipodal points to the same point.
  • B. Knaster–Ulam theorem
    The Knaster–Ulam theorem is a result in topology and measure theory that, roughly speaking, guarantees the existence of points with certain symmetry or invariance properties under measure-preserving transformations.
  • C. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • D. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

Stage Batch ID Job type Status
creating batch_69e0b50438e08190917e2538bb8bc034 elicitation completed
NER batch_69e6fcf4d26481908b639996500a8319 ner completed
Created at: April 16, 2026, 2:34 p.m.