Smoothness of sets in Euclidean spaces
arXiv:1009.4446 · doi:10.1112/blms/bdq121
Abstract
We study some properties of smooth sets in the sense defined by Hungerford. We prove a sharp form of Hungerford's Theorem on the Hausdorff dimension of their boundaries on Euclidean spaces and show the invariance of the definition under a class of automorphisms of the ambient space.
11 pages, 1 figure. To appear on the Bulletin of the London Mathematical Society