Whitney embedding theorem information

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

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

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...

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

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

Whitehead theorem (homotopy theory) Whitney embedding theorem (differential manifolds) Whitney extension theorem (mathematical analysis) Whitney immersion...

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

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

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

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

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...

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

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

metric on M {\displaystyle M} . An alternative proof uses the Whitney embedding theorem to embed M {\displaystyle M} into Euclidean space and then pulls back...

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

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

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

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...

the Whitney embedding theorem, every manifold admits a normal bundle, given such an embedding. There is in general no natural choice of embedding, but...

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

in the Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric C1 embedding theorem and the Smale–Hirsch immersion theorem. Assume...