Triple

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).

Phrase: Baire category theorem | Statement: [open mapping theorem, proofTechnique, Baire category theorem]

Target entity: Baire category theorem
Context triple: [open mapping theorem, proofTechnique, 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.