In mathematics, Sard's theorem, also known as Sard's lemma or the Morse–Sard theorem, is a result in mathematical analysis that asserts that the set of...

differentiable. Such a retraction must have a non-singular value, by Sard's theorem, which is also non-singular for the restriction to the boundary (which...

Sahlqvist correspondence theorem (modal logic) Saint-Venant's theorem (physics) Sard's theorem (differential geometry) Sarkovskii's theorem (dynamical systems)...

given above is the more commonly used; e.g., in the formulation of Sard's theorem. Given a submersion between smooth manifolds f : M → N {\displaystyle...

Zbl 0101.16103. Smale, S. (1965). "An infinite dimensional version of Sard's theorem". Amer. J. Math. 87 (4): 861–866. doi:10.2307/2373250. JSTOR 2373250...

theorem. Alternatively, the requirement that det(Dφ) ≠ 0 can be eliminated by applying Sard's theorem. For Lebesgue measurable functions, the theorem...

embedding theorem Critical value Sard's theorem Saddle point Morse theory Lie derivative Hairy ball theorem Poincaré–Hopf theorem Stokes' theorem De Rham...

requires more sophisticated results from mathematical analysis such as Sard's theorem and the coarea formula. In even greater generality, using the Lebesgue...

nullcline or some other curve describing terminal conditions. Using Sard's theorem, whose hypothesis is a special case of the transversality of maps, it...

the field that has connections, for example, to rectifiability and Sard's theorem. Definition: Given f : R n → R m {\displaystyle f\colon \mathbb {R}...