Triple

T16249734
Position Surface form Disambiguated ID Type / Status
Subject Banach–Steinhaus theorem E394468 entity
Predicate requires P100 FINISHED
Object Baire category theorem E518477 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Baire category theorem | Statement: [Banach–Steinhaus theorem, requires, Baire category theorem]

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: Baire category theorem
Context triple: [Banach–Steinhaus theorem, requires, Baire category theorem]
  • A. Baire category theorem chosen
    The Baire category theorem is a fundamental result in topology and functional analysis stating that complete metric (or locally compact Hausdorff) spaces cannot be written as countable unions of nowhere dense sets, with powerful consequences for the structure of such spaces.
  • B. Baire space
    Baire space is a fundamental topological space—typically the set of all infinite sequences of natural numbers with the product topology—that serves as a central object in descriptive set theory and general topology.
  • C. Banach–Steinhaus theorem
    The Banach–Steinhaus theorem is a fundamental result in functional analysis that characterizes when a family of continuous linear operators is uniformly bounded, with major implications for the behavior of sequences of operators on Banach spaces.
  • D. Lusin–Souslin theorem
    The Lusin–Souslin theorem is a fundamental result in descriptive set theory stating that the continuous injective image of a Borel set in a Polish space is again a Borel set.
  • E. Borel–Lebesgue theorem
    The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69d87f2171208190951025e526947816 elicitation completed
NER batch_69e2459606f88190a53905186f7f73be ner completed
NED1 batch_6a000ee568a48190835ce76f84461044 ned_source_triple completed
Created at: April 10, 2026, 5:04 a.m.