In this paper, we study the concepts of Wijsman statistical convergence, Hausdorff statistical convergence and  Wijsman statistical Cauchy double sequences of sets and investigate the relationship between them.

We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assume the Hausdorff functions are continuous or blanketed, and we do not assume the metric space is a subset of Euclidean space. We discuss the covering measure (= centered Hausdorff measure) and packing...

In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the “multiplicative golden mean shift” defined as the set of all reals in [0, 1] whose binary expansion (xk) satisfies xkx2k = 0 for all k ≥ 1. Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obta...

We prove that the maximal Hausdorff compactification χf of a T2-compactifiable mapping f and the maximal Tychonoff compactification βf of a Tychonoff mapping f (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a T2-compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of...

In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. In particular, we prove that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal upper Rényi dimensions. As an application we get a continuity pr...

O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Cech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space (X, t) can be embedded as a dense subspace of a compact, Hausdorff, limit space (Xi, ri) with the following property: any continuous function from (X, t) into a compact, Hau...

The famous game Towers of Hanoi is related with a family of so–called Hanoi–graphs. We regard these non self–similar graphs as geometrical objects and obtain a sequence of fractals (HGα)α converging to the Sierpiński gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does co...

In this note we define a rather pathological connectedness property of Hausdorff spaces which is stronger than ordinary connectedness. We obtain a few basic properties of such spaces and derive a method for constructing them. It turns out that countable Hausdorff spaces having the connectedness property are as easily constructed as uncountable ones. Hence we have still another method for constr...

The paper investigates bounds on various notions of complexity for ω–languages. We understand the complexity of an ω–languages as the complexity of the most complex strings contained in it. There have been shown bounds on simple and prefix complexity using fractal Hausdorff dimension. Here these bounds are refined by using general Hausdorff measure originally introduced by Felix Hausdorff. Furt...

This paper proposes an oriented Hausdorff similarity measure for object matching. The oriented Hausdorff distance (HD) measure is introduced by replacing the distance concept of conventional HD algorithms by a similarity measure. The orientation at each ~ i x e l is used for removing incorrect correspondences. Various experiments show that the perFigure 1: Block diagram for the Hausdorff distan...