In this paper, we give important properties as completeness, completion and precompactness of Hausdorff intuitionistic fuzzy metric spaces which is given by Gregori et al [13] and establish the precise relationship between the Hausdorff metric of a metric space (X, d) and the Hausdorff intuitionistic fuzzy metric of the standart intuitionistic fuzzy metric of d, and give two examples. AMS Subje...

This paper defines and discusses the Hausdorff metric on the space of nonempty, closed, and bounded subsets of a given metric space. We consider two important topological properties, completeness and total boundedness. We prove that each of these properties is posessed by a Hausdorff metric space if the property is possesed by the underlying metric space. Finally, we explore applications of the...

Let Y be a proximinal subspace of finite codimension of c0. We show that Y is proximinal in ∞ and the metric projection from ∞ onto Y is Hausdorff metric continuous. In particular, this implies that the metric projection from ∞ onto Y is both lower Hausdorff semi-continuous and upper Hausdorff semi-continuous.

We extend the Voronoi diagram framework to compute the critical area of a circuit layout [15, 12, 16, 13, 14] with the ability to accurately compute critical area for via-blocks on via and contact layers in the presence of multilayer loops, redundant vias, and redundant interconnects. Critical area is a measure reflecting the sensitivity of a VLSI design to random defects during IC manufacturin...

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the ex...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the ...

We revisit the L∞ Hausdorff Voronoi diagram of clusters of points, equivalently, the L∞ Hausdorff Voronoi diagram of rectangles, and present a plane sweep algorithm for its construction that generalizes and improves upon previous results. We show that the structural complexity of the L∞ Hausdorff Voronoi diagram is Θ(n+m), where n is the number of given clusters and m is the number of essential...

We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subsets. As a consequence, we deduce the corresponding result for metric spaces by using the standard...

We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once punctured torus and the 4–times punctured sphere. For these two surfaces, we also compute the Hausdorff dimension of the space of geodesic laminations, when it is endowed with the natural metric which, for small distances, is ...