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Ultrametric spaces bi-Lipschitz embeddable in n

Kerkko Luosto (1996)

Fundamenta Mathematicae

It is proved that if an ultrametric space can be bi-Lipschitz embedded in n , then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in n .

Ultrasmoothness in dendroids

Isabel Puga, Miriam Torres (2008)

Colloquium Mathematicae

The class of ultrasmooth dendroids is contained in the class of smooth dendroids and contains the class of locally connected dendroids. In this paper we study relationships between ultrasmoothness and smoothness in dendroids and we characterize ultrasmooth dendroids.

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