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.