Smoothness of sets in Euclidean spaces

Details Smoothness of sets in Euclidean spaces Smoothness of sets in Euclidean spaces

2010-09-22

arxiv.org/abs/1009.4446v2

Mathematics

Classical Analysis and ODEs

11 pages, 1 figure. To appear on the Bulletin of the London Mathematical Society

Scientific paper

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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