Whitney extension theorem

Target entity: Whitney extension theorem
Context triple: [Hassler Whitney, notableFor, Whitney extension theorem]

• A. Calderón interpolation theorem
  The Calderón interpolation theorem is a fundamental result in functional analysis that provides a powerful method for constructing intermediate spaces and extending bounded linear operators between them.
• B. Stone–Weierstrass theorem
  The Stone–Weierstrass theorem is a fundamental result in functional analysis that characterizes when a subalgebra of continuous functions on a compact space is dense, thereby generalizing classical polynomial approximation results.
• C. Weierstrass approximation theorem
  The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
• D. Paley–Wiener theorem
  The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
• E. Singular Integrals and Differentiability Properties of Functions
  "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Whitney extension theorem
Target entity description: The Whitney extension theorem is a fundamental result in mathematical analysis that characterizes when a function defined on a closed subset of Euclidean space can be extended to a smooth function on the whole space.

• A. Calderón interpolation theorem
  The Calderón interpolation theorem is a fundamental result in functional analysis that provides a powerful method for constructing intermediate spaces and extending bounded linear operators between them.
• B. Stone–Weierstrass theorem
  The Stone–Weierstrass theorem is a fundamental result in functional analysis that characterizes when a subalgebra of continuous functions on a compact space is dense, thereby generalizing classical polynomial approximation results.
• C. Weierstrass approximation theorem
  The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
• D. Paley–Wiener theorem
  The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
• E. Singular Integrals and Differentiability Properties of Functions
  "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
• F. None of above. chosen