On the immersion of an π-dimensional manifold in π+1-dimensional Euclidean space
Benjamin R. Halpern Β· Proceedings of the American Mathematical Society Β· 1971
Consider the subset of n + 1 n + 1 -dimensional Euclidean space swept out by the tangent hyperplanes drawn through the points of an immersed compact closed connected n -dimensional smooth manifold. If this is not all of the Euclidean space, then the manifold is diffeomorphic to a sphere, the immersion is an embedding, the image of the immersion is the boundary of a unique open starshaped set, and the set of points not on any tangent hyperplane is the interior of the kernel of the open starshaped set. A converse statement also holds.