Smoothness of sets in Euclidean spaces

Artur Nicolau; Daniel Seco

doi:https://doi.org/10.1112/blms/bdq121

Smoothness of sets in Euclidean spaces

Artur Nicolau, Daniel Seco

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

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. © 2011 London Mathematical Society.

Original language	English
Pages (from-to)	536-546
Journal	Bulletin of the London Mathematical Society
Volume	43
DOIs	https://doi.org/10.1112/blms/bdq121
Publication status	Published - 1 Jan 2011

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title = "Smoothness of sets in Euclidean spaces",

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. {\textcopyright} 2011 London Mathematical Society.",

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AB - 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. © 2011 London Mathematical Society.

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JO - Bulletin of the London Mathematical Society

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Smoothness of sets in Euclidean spaces

Abstract

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