  Let n be aninteger>4. There is a smoothly knotted n-dimensional sphere in
(n+2)-space such that the singular point set of its projection in (n+1)-space
consists of double points and that the components of the singular point set are
two. (The sphere is knotted in the sense that it does not bound any embedded
(n+1)-ball in (n+2)-space.) Furthermore, the projection is not the projection
of any unknotted sphere in the (n+2)-space. There are two inequivalent
embeddings of an n-manifold in the (n+2)-space such that the projection of one
of these in (n+1)-space has no double points and the projection of the other
has a connected embedded double point set.
