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Whitney-type extensions in quasi-metric spaces

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  • We discuss geometrical scenarios guaranteeing that functions defined on a given set may be extended to the entire ambient, with preservation of the class of regularity. This extends to arbitrary quasi-metric spaces work done by E.J. McShane in the context of metric spaces, and to geometrically doubling quasi-metric spaces work done by H. Whitney in the Euclidean setting. These generalizations are quantitatively sharp.
    Mathematics Subject Classification: Primary: 26A16, 26B35; Secondary 26B05, 54E35.

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