Hausdorff maximal principle

Target entity: Hausdorff maximal principle
Context triple: [Felix Hausdorff, notableConcept, Hausdorff maximal principle]

• A. 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.
• B. Krein–Milman theorem
  The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
• C. 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.
• D. Alexandrov–Hausdorff theorem
  The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
• E. Cantor–Bernstein–Schröder theorem
  The Cantor–Bernstein–Schröder theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hausdorff maximal principle
Target entity description: The Hausdorff maximal principle is a foundational result in set theory and order theory stating that every partially ordered set contains a maximal totally ordered subset (a maximal chain), and it is equivalent to the axiom of choice.

• A. 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.
• B. Krein–Milman theorem
  The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
• C. 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.
• D. Alexandrov–Hausdorff theorem
  The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
• E. Cantor–Bernstein–Schröder theorem
  The Cantor–Bernstein–Schröder theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen