Coincidence of Vietoris and Wijsman Topologies: A New Proof

Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies on CL(X) coincide.

Intelligent System for Computer Aided Assembly Process Planning

This paper presents the concepts of the intelligent system for aiding of the module assembly technology. The first part of this paper presents a project of intelligent support system for computer aided assembly process planning. The second part includes a coincidence description of the chosen aspects of implementation of this intelligent system using technologies of artificial intelligence (artificial neural networks, fuzzy logic, expert systems and genetic algorithms).