Editing Whitney embedding theorem (section)

==Isotopy versions==
A relatively 'easy' result is to prove that any two embeddings of a 1-manifold into {{tmath|\R^4}} are isotopic (see [[Knot theory#Higher dimensions]]). This is proved using general position, which also allows to show that any two embeddings of an {{mvar|n}}-manifold into {{tmath|\R^{2n+2} }} are isotopic. This result is an isotopy version of the weak Whitney embedding theorem.

Wu proved that for {{math|''n'' ≥ 2}}, any two embeddings of an {{mvar|n}}-manifold into {{tmath|\R^{2n+1} }} are isotopic. This result is an isotopy version of the strong Whitney embedding theorem.

As an isotopy version of his embedding result, [[André Haefliger|Haefliger]] proved that if {{mvar|N}} is a compact {{mvar|n}}-dimensional {{mvar|k}}-connected manifold, then any two embeddings of {{mvar|N}} into {{tmath|\R^{2n-k+1} }} are isotopic provided {{math|2''k'' + 2 ≤ ''n''}}. The dimension restriction {{math|2''k'' + 2 ≤ ''n''}} is sharp: Haefliger went on to give examples of non-trivially embedded 3-spheres in {{tmath|\R^6}} (and, more generally, {{math|(2''d'' − 1)}}-spheres in {{tmath|\R^{3d} }}). See [http://www.map.mpim-bonn.mpg.de/High_codimension_embeddings:_classification further generalizations].