Displaying similar documents to “The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors”

Transverse Hausdorff dimension of codim-1 C2-foliations

Takashi Inaba, Paweł Walczak (1996)

Fundamenta Mathematicae

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The Hausdorff dimension of the holonomy pseudogroup of a codimension-one foliation ℱ is shown to coincide with the Hausdorff dimension of the space of compact leaves (traced on a complete transversal) when ℱ is non-minimal, and to be equal to zero when ℱ is minimal with non-trivial leaf holonomy.

On finite-dimensional maps and other maps with "small" fibers

Yaki Sternfeld (1995)

Fundamenta Mathematicae

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We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in I k such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional.  These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional...