Sard's theorem

E960598 UNEXPLORED

Sard's theorem is a fundamental result in differential topology stating that the set of critical values of a smooth map between manifolds has measure zero, implying that almost all values are regular.

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All labels observed (3)

Label	Occurrences
Sard's theorem canonical	3
Sard–Smale theorem	1
Sard’s theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T12011793 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Sard's theorem
Context triple: [Differential Topology (book), topic, Sard's theorem]

A. Thom transversality theorem
The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
B. Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
C. Whitney embedding theorem
The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
D. Darboux theorem
The Darboux theorem is a fundamental result in symplectic geometry stating that all symplectic manifolds are locally symplectomorphic to the standard symplectic space, implying that the symplectic form can always be put into a canonical local normal form.
E. Poincaré–Hopf theorem
The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Sard's theorem
Target entity description: Sard's theorem is a fundamental result in differential topology stating that the set of critical values of a smooth map between manifolds has measure zero, implying that almost all values are regular.

A. Thom transversality theorem
The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
B. Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
C. Whitney embedding theorem
The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
D. Darboux theorem
The Darboux theorem is a fundamental result in symplectic geometry stating that all symplectic manifolds are locally symplectomorphic to the standard symplectic space, implying that the symplectic form can always be put into a canonical local normal form.
E. Poincaré–Hopf theorem
The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
F. None of above. chosen