A remarkable and elementary fact that a locally compact set F of Euclidean space is a smooth manifold if (and only if) the lower and upper paratangent cones to F coincide at every point, is proved. The celebrated von Neumann’s result (1929) that a locally compact subgroup of the general linear group is a smooth manifold, is a straightforward application.
Geometric characterizations of C1 manifolds in Euclidean spaces by tangent cones
Bigolin, Francesco;Greco, Gabriele Hans
2012-01-01
Abstract
A remarkable and elementary fact that a locally compact set F of Euclidean space is a smooth manifold if (and only if) the lower and upper paratangent cones to F coincide at every point, is proved. The celebrated von Neumann’s result (1929) that a locally compact subgroup of the general linear group is a smooth manifold, is a straightforward application.File in questo prodotto:
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