Displaying similar documents to “Every graph is a self-similar set.”

An invariant of bi-Lipschitz maps

Hossein Movahedi-Lankarani (1993)

Fundamenta Mathematicae

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A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set 0 ∪ 1 / n n ≥ 1 is Lipschitz isomorphic to an ultrametric...

Extension and reconstruction theorems for the Urysohn universal metric space

Wiesław Kubiś, Matatyahu Rubin (2010)

Czechoslovak Mathematical Journal

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We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.

On metric products

Irmina Herburt, Maria Moszyńska (1991)

Colloquium Mathematicae

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