Triple

T21047164
Position Surface form Disambiguated ID Type / Status
Subject Baire category theorem E518477 entity
Predicate relatedTo P37 FINISHED
Object Baire space (topology) — NE NERFINISHED

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 space (topology) | Statement: [Baire category theorem, relatedTo, Baire space (topology)]

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 space (topology)
Context triple: [Baire category theorem, relatedTo, Baire space (topology)]
  • A. 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.
  • B. Baire category theorem
    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.
  • C. Baire space ω^ω chosen
    Baire space ω^ω is a fundamental topological space consisting of all infinite sequences of natural numbers with the product topology, serving as a central object in descriptive set theory and topology.
  • D. Tychonoff space
    A Tychonoff space is a topological space that is both completely regular and Hausdorff, forming a central class in general topology with strong separation and embedding properties.
  • E. Banach–Mazur game
    The Banach–Mazur game is an infinite two-player topological game used to characterize properties such as Baire category and completeness in metric and topological spaces.
  • 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.