Editing Whitney immersion theorem (section)

{{short description|On immersions of smooth  m-dimensional manifolds in 2m-space and (2m-1) space}}
In [[differential topology]], the '''Whitney immersion theorem''' (named after [[Hassler Whitney]]) states that for <math>m>1</math>, any smooth <math>m</math>-dimensional [[manifold]] (required also to be [[Hausdorff space|Hausdorff]] and [[second-countable]]) has a one-to-one [[immersion (mathematics)|immersion]] in [[Euclidean space|Euclidean]] <math>2m</math>-space, and a (not necessarily one-to-one) immersion in <math>(2m-1)</math>-space. Similarly, every smooth <math>m</math>-dimensional manifold can be immersed in the <math>2m-1</math>-dimensional sphere (this removes the <math>m>1</math> constraint).

The weak version, for <math>2m+1</math>, is due to [[Transversality (mathematics)|transversality]] ([[general position]], [[dimension counting]]): two ''m''-dimensional manifolds in <math>\mathbf{R}^{2m}</math> intersect generically in a 0-dimensional space.