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Displaying similar documents to “Transverse Hausdorff dimension of codim-1 C2-foliations”

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.

Ordinal products of topological spaces

Vitalij Chatyrko (1994)

Fundamenta Mathematicae

Similarity:

The notion of the ordinal product of a transfinite sequence of topological spaces which is an extension of the finite product operation is introduced. The dimensions of finite and infinite ordinal products are estimated. In particular, the dimensions of ordinary products of Smirnov's [S] and Henderson's [He1] compacta are calculated.

A dimension raising hereditary shape equivalence

Jan Dijkstra (1996)

Fundamenta Mathematicae

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We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.

Universal spaces in the theory of transfinite dimension, I

Wojciech Olszewski (1994)

Fundamenta Mathematicae

Similarity:

R. Pol has shown that for every countable ordinal α, there exists a universal space for separable metrizable spaces X with ind X = α . We prove that for every countable limit ordinal λ, there is no universal space for separable metrizable spaces X with Ind X = λ. This implies that there is no universal space for compact metrizable spaces X with Ind X = λ. We also prove that there is no universal space for compact metrizable spaces X with ind X = λ.

Minimal periods of maps of rational exterior spaces

Grzegorz Graff (2000)

Fundamenta Mathematicae

Similarity:

The problem of description of the set Per(f) of all minimal periods of a self-map f:X → X is studied. If X is a rational exterior space (e.g. a compact Lie group) then there exists a description of the set of minimal periods analogous to that for a torus map given by Jiang and Llibre. Our approach is based on the Haibao formula for the Lefschetz number of a self-map of a rational exterior space.

Dynamical boundary of a self-similar set

Manuel Morán (1999)

Fundamenta Mathematicae

Similarity:

Given a self-similar set E generated by a finite system Ψ of contracting similitudes of a complete metric space X we analyze a separation condition for Ψ, which is obtained if, in the open set condition, the open subset of X is replaced with an open set in the topology of E as a metric subspace of X. We prove that such a condition, which we call the restricted open set condition, is equivalent to the strong open set condition. Using the dynamical properties of the forward shift, we find...