Publication:
Smoothness of sets in Euclidean spaces

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2011-06
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London Mathematical Society
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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.
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Nicolau, A. & Seco, D. (2011). Smoothness of sets in Euclidean spaces. Bulletin of the London Mathematical Society, 43(3), pp. 536–546.