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: [Closed Graph Theorem, relatedTo, Uniform Boundedness Principle]

Target entity: Uniform Boundedness Principle
Context triple: [Closed Graph Theorem, relatedTo, 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. Banach–Saks theorem
  The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.