Displaying similar documents to “On the Lavrentieff phenomenon for some classes of Dirichlet minimum points.”

Minimal bi-Lipschitz embedding dimension of ultrametric spaces

Jouni Luukkainen, Hossein Movahedi-Lankarani (1994)

Fundamenta Mathematicae

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We prove that an ultrametric space can be bi-Lipschitz embedded in ℝ n if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

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The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain