If the set of monomorphisms between locally convex spaces is not empty, then it is an open subset of the space of all continuous and linear operators endowed with the topology of the uniform convergence on the bounded sets if and only if the domain space is normable. The corresponding characterization for the set of almost open operators is also obtained; it is related to the lifting of bounded...

The particle swarm optimization (PSO) algorithm, in which individuals collaborate with their interacted neighbors like bird flocking to search for the optima, has been successfully applied in a wide range of fields pertaining to searching and convergence. Here we employ the scale-free network to represent the inter-individual interactions in the population, named SF-PSO. In contrast to the trad...

This paper investigates the behavior of the Hausdorr dimensions of the limit sets n and of a sequence of Kleinian groups ? n ! ?, where M = H 3 =? is geometrically nite. We show if ? n ! ? strongly, then: (a) M n = H 3 =? n is geometrically nite for all n 0, (b) n ! in the Hausdorr topology, and (c) H: dim((n) ! H: dim((), if H: dim(() 1. On the other hand, we give examples showing the dimensio...

This is a study of metric spaces, a subject originally initiated by Maurice Fréchet in 1906 and subsequently developed by Hausdorff, Riesz, and ultimately Banach. The original motivation behind the theory idea was to extend the notion of convergence from the real and complex field to more abstract spaces. The idea of the metric was used by Fréchet to induce a topology on the space and later thi...

Economic disparities between the regions of the European Union are of constant concern both for policy and economic research. In this paper we examine whether there are overlapping trends of regional development in the EU: overall convergence on the one hand and persistent or even increasing spatial concentration (agglomeration) on the other. Kernel density estimation, Markov chain analysis and...

The issue of convergence or divergence of productivity has important policy for regional poverty reduction and increasing standards of living. If productivity converges to a common level without intervention, there is little need for explicit policies in lagging regions to promote catch up. On the other hand, productivity has divergence trend, then explicit policies would be needed to prevent f...