differential topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real...

M} with box counting dimension dA. Using ideas from Whitney's embedding theorem, A can be embedded in k-dimensional Euclidean space with k > 2 d A . {\displaystyle...

Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into...

01016. Loomis–Whitney inequality Whitney extension theorem Stiefel–Whitney class Whitney's conditions A and B Whitney embedding theorem Whitney graph isomorphism...

Waldhausen's theorem (geometric topology) Whitney embedding theorem (differential manifolds) Whitney immersion theorem (differential topology) Radó's theorem (harmonic...

In mathematics, the Mostow–Palais theorem is an equivariant version of the Whitney embedding theorem. It states that if a manifold is acted on by a compact...

Famous theorems in differential topology include the Whitney embedding theorem, the hairy ball theorem, the Hopf theorem, the Poincaré–Hopf theorem, Donaldson's...

n} must be for an embedding, in terms of the dimension m {\displaystyle m} of M {\displaystyle M} . The Whitney embedding theorem states that n = 2 m...

In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for m > 1 {\displaystyle m>1} , any smooth m {\displaystyle...

GitHub) Manifold hypothesis Spectral submanifold Taken's theorem Whitney embedding theorem Discriminant analysis Elastic map Feature learning Growing...

surfaces in the extrinsic sense. However, the Whitney embedding theorem asserts every surface can in fact be embedded homeomorphically into Euclidean space,...

planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the...

the modern study of both fields. Embed M in some high-dimensional Euclidean space. (Use the Whitney embedding theorem.) Take a small neighborhood of M...

ramified covering spaces. Basic results include the Whitney embedding theorem and Whitney immersion theorem. In complex geometry, ramified covering spaces...

ramified covering spaces. Basic results include the Whitney embedding theorem and Whitney immersion theorem. In Riemannian geometry, one may ask for maps to...

because, by the Whitney embedding theorem, any second-countable smooth (abstract) m {\displaystyle m} -manifold can be smoothly embedded in R 2 m {\displaystyle...

because the Whitney embedding theorem, the key technical trick which underlies surgery theory, requires 2+1 dimensions. Roughly, the Whitney trick allows...

full and faithful limit-preserving embedding of any category into a category of presheaves. Mitchell's embedding theorem for abelian categories realises...

immersion, and in fact to an embedding for 2m < n; these are the Whitney immersion theorem and Whitney embedding theorem. Stephen Smale expressed the...

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

manifolds. For example, the Whitney embedding theorem tells us that every smooth n-dimensional manifold can be embedded as a smooth submanifold of R2n...

use of a partition of unity. An alternative proof uses the Whitney embedding theorem to embed M {\displaystyle M} into Euclidean space and then pulls back...

the Nash embedding theorem can be assumed. However, this theorem was not available then, as John Nash published his famous embedding theorem for Riemannian...

derivative never vanishes.) The Whitney embedding theorem tells us that every smooth n-dimensional manifold can be embedded as a smooth submanifold of R...

embeddings and immersions include: Whitney embedding theorem Whitney immersion theorem Nash embedding theorem Smale-Hirsch theorem Key tools in studying these...

a cancelling pair as desired, so long as we can embed this disk into the boundary of W. This embedding exists if dim ⁡ ∂ W − 1 = n − 1 ≥ 2 ( k + 1 ) {\displaystyle...

fixed-point theorem Chern's conjecture (affine geometry) Differential structure Homotopy principle Immersion (mathematics) Whitney embedding theorem The Cr...

{R} ^{2n+1}} , proved by combining Whitney embedding theorem for manifolds and the universal approximation theorem for neural networks. To regularize...

h-cobordism theorem, where it is used to cancel the intersection points; and its failure in low dimensions corresponds to not being able to embed a Whitney disc...

are equivalent by regular homotopy, though not by isotopy. The Whitney–Graustein theorem classifies the regular homotopy classes of a circle into the plane;...