We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric dH and with a variation of this metric called the dlog metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks. AMS Classification numbers Primary: 57M99

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some...

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 the paper, we introduce the concepts of dynamic object identification and verification using video. A generalized Hausdorff metric, which is more robust to noise and allows a confidence interpretation, is suggested for the identification and verification problem. Parameters from sensor motion compensation procedure are incorporated into the search step such that the Hausdorff metric based ma...

Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek’s sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasipseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this struc...

Hyperspace theory has its beginnings in the early years of XX century with the work of Felix Hausdorff (1868-1942) and Leopold Vietoris (1891-2002). Given a topological space X, the hyperspace 2X of all nonempty closed subsets of X is equipped with the Vietoris topology, also called the exponential topology, see [37, p. 160] or the finite topology, see [48, p. 153], introduced in 1922 by Vietor...