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: Lusternik–Schnirelmann category | Statement: [Lazar Lyusternik, notableConcept, Lusternik–Schnirelmann category]

Target entity: Lusternik–Schnirelmann category
Context triple: [Lazar Lyusternik, notableConcept, Lusternik–Schnirelmann category]

• A. Lusternik–Schnirelmann category chosen
  The Lusternik–Schnirelmann category is a numerical homotopy invariant of a topological space that measures the minimal number of contractible open sets needed to cover it, playing a key role in critical point theory and algebraic topology.
• B. Leray–Schauder degree
  The Leray–Schauder degree is a topological invariant that generalizes the Brouwer degree to compact perturbations of the identity in infinite-dimensional Banach spaces, providing a powerful tool for proving existence of solutions to nonlinear equations.
• C. Alexandrov–Čech cohomology
  Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
• D. Lefschetz fixed-point theorem
  The Lefschetz fixed-point theorem is a fundamental result in algebraic topology that relates the number of fixed points of a continuous map on a topological space to traces of the induced maps on its homology groups.
• E. Morse Theory
  Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.