In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for
-dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean
, is due to transversality (general position, dimension counting): two m-dimensional manifolds in
intersect generically in a 0-dimensional space.
William S. Massey (Massey 1960) went on to prove that every n-dimensional manifold is cobordant to a manifold that immerses in
is the number of 1's that appear in the binary expansion of
In the same paper, Massey proved that for every n there is manifold (which happens to be a product of real projective spaces) that does not immerse in
The conjecture that every n-manifold immerses in
This conjecture was eventually solved in the affirmative by Ralph Cohen (1985).
This topology-related article is a stub.