This result is used to prove a theorem stating that every Riemannian manifold can have the length of their paths preserved while undergoing the namesake operation - that theorem based on this one was proved by John Nash.
A variant of this result that applies to certain orbit types is the Mostow-Palais Theorem. The elimination of opposite-signed double points by this statement shows that the set of certain equivalence relations between manifolds is C-isomorphic to the cylinder defined by "M sub zero, cross the unit interval". This result is used to prove a theorem stating that every Riemannian manifold can have the length of their paths preserved while undergoing the namesake operation - that theorem based on this one was proved by John Nash. As a result of this theorem, every compact manifold admits a normal vector bundle. Smale's proof of the h-cobordism theorem relies on this theorem's "trick". It relies on the "weak immersion theorem" also proved by this theorem's namesake. For 10 points, name this theorem stating that every smooth n-manifold can be fixed in R to the "2n plus 1."
A variant of this result that applies to certain orbit types is the Mostow-Palais Theorem.
Whitney embedding theorem [prompt on embedding theorem or Whitney’s Theorem]