|ISSN 1088-6826(online) ISSN 0002-9939(print)|
On the immersion of an -dimensional manifold in -dimensional Euclidean space
Abstract: Consider the subset of -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.
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