Sublinear Higson corona and Lipschitz extensions

• Autores: Matija Cencelj, Jerzy Dydak, Ales Vavpetic
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 4, 2011, págs. 1307-1322
• Idioma: inglés
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• Resumen

  • We show that the dimension of the sublinear Higson corona of a metric space X is the smallest non-negative integer m with the following property: Any norm-preserving asymptotically Lipschitz function from a closed subset A of X to the Euclidean space of dimension m+1 extends to a norm-preserving asymptotically Lipschitz function from X to the Euclidean space of dimension m+1. As an application we obtain another proof of the following result of Dranishnikov and Smith: Let X be a cocompact proper metric space, which is M-connected for some M, and has the asymptotic Assouad-Nagata dimension finite. Then this dimension equals the dimension of the sublinear Higson corona of X