‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the c...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves. It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance. Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given...

In sub-Riemannian geometry, the length of a non-horizontal path is not defined (or is equal to +∞). However several other notions allow to measure a path, such as the Hausdorff measures, the class of k-dimensional lengths introduced in [2], or notions based on approximations by discrete sets, like the nonholonomic interpolation complexity and the entropy (see [8, 10]). The purpose of this paper...