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Displaying 841 – 860 of 3924

Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...

Covering spaces and irreducible partitions

D. J. Grubb (2011)

Fundamenta Mathematicae

An irreducible partition of a space is a partition of that space into solid sets with a certain minimality property. Previously, these partitions were studied using the cup product in cohomology. This paper obtains similar results using the fundamental group instead. This allows the use of covering spaces to obtain information about irreducible partitions. This is then used to generalize Knudsen's construction of topological measures on the torus. We give examples of such measures that are invariant...

Covering the real line with translates of a zero-dimensional compact set

András Máthé (2011)

Fundamenta Mathematicae

We construct a compact set C of Hausdorff dimension zero such that cof(𝒩) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.

Covering theorems for uniqueness and extended uniqueness sets

Alexander S. Kechris, Alain Louveau (1990)

Colloquium Mathematicae

Criterios de convergencia de medidas de conjuntos Riemann integrables.

Pedro Jiménez Guerra (1980)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

In some recent work, fractal curvatures $C_{k}^{f} (F)$ and fractal curvature measures $C_{k}^{f} (F, \cdot)$ , $k = 0, ..., d$ , have been determined for all self-similar sets $F$ in $ℝ^{d}$ , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations...

Curvature integral and Lipschitz parametrization in 1-regular metric spaces.

Hahlomaa, Immo (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

Curvature measures and fractals [Book]

Steffen Winter (2008)

We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.