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...

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.

This paper presents a novel approach for resource finding and job allocation in a computational Grid. The proposed system is called HYGRA, for HYperspace-based Grid Resource Allocation. The basic principle involves the construction of a virtual hyperspace in which the available amount of each resource type is used as a geometric coordinate, making each Grid node representable as a point in this...

Instantaneous noise-based logic can avoid time-averaging, which implies significant potential for low-power parallel operations in beyond-Moore-law-chips. However, in its randomtelegraph-wave representation, the complete uniform superposition (superposition of all N-bit binary numbers) will be zero with high probability, that is, non-zero with exponentially low probability, thus operations with...

We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f : X ! X on a metric space X, we study the extended dynamical systems (V X; V f), (UX; Uf) and (LX;Lf) where V , U and L are respectively the Vietoris hyperspace, the upper hyperspace and the lower hyperspace functors....

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

An estimate for the Novak number of a hyperspace with the Vietoris topology is given. As a consequence it is shown that this cardinal function can decrease passing from a space to its hyperspace.

An object-space hidden-line algorithm for higher-dimensional scenes has been designed and implemented. Scenes consist of convex hulls of any dimension, each of which is compared against the edges of all convex hulls not eliminated by a hyperdimensional clipper, a depth test after sorting and a minimax text. Hidden and visible elements are determined in accordance with the dimensionality of the ...