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Two ideals connected with strong right upper porosity at a point

Viktoriia Bilet;  Oleksiy Dovgoshey;  Jürgen Prestin — 2015

Czechoslovak Mathematical Journal

Let SP be the set of upper strongly porous at 0 subsets of ℝ + and let I ^ ( SP ) be the intersection of maximal ideals I ⊆ SP . Some characteristic properties of sets E ∈ I ^ ( SP ) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of ℝ + is a proper subideal of I ^ ( SP ) . Earlier, completely strongly porous sets and some of their properties were...

Linear distortion of Hausdorff dimension and Cantor's function.

Oleksiy Dovgoshey;  Vladimir Ryazanov;  Olli Martio;  Matti Vuorinen — 2006

Collectanea Mathematica

Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and H(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that H(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every...

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