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: Uniform boundedness principle | Statement: [Baire category theorem, hasConsequence, Uniform boundedness principle]

Target entity: Uniform boundedness principle
Context triple: [Baire category theorem, hasConsequence, Uniform boundedness principle]

• A. Banach–Steinhaus theorem chosen
  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.
• B. Banach–Alaoglu theorem
  The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
• C. Arzelà–Ascoli theorem
  The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
• D. Banach inverse mapping theorem
  The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
• E. Hahn–Banach theorem
  The Hahn–Banach theorem is a fundamental result in functional analysis that guarantees the extension of bounded linear functionals from a subspace to the whole space without increasing their norm.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.