Convergence of a sequence of deterministic functions in the Skorohod topology d…‰0;?†† implies convergence of the jumps. For processes with independent additive increments the ®xed discontinuities converge. In this paper it will be shown that this is not true for processes with independent max-increments. The limit in d…‰0;?†† of a sequence of stochastically continuous extremal processes may ha...

This is a preliminary report on the continuous action of convergence groups on convergence spaces. In particular, the convergence structure on the homeomorphism group and its continuous action are investigated in this paper. Also, attempts have been made to establish a one-to-one correspondence between continuous action of a convergence group and its homeomorphic representation on a convergence

The axioms for a topology in terms of open sets follow necessarily from the intuitive relation of this concept with ultrafilter convergence. By contrast, the intuitive relations between neighbourhood systems or closure operations on the one hand and ultrafilter convergence on the other lead only to pretopologies. Kleisli operations, previously used in categorical algebra, greatly facilitate cat...

The note contains two examples of function spaces Cp(X) endowed with the pointwise topology. The first example is Cp(M),M being a planar continuum, such that Cp(M) is uniformly homeomorphic to Cp(M) if and only ifm = n. This strengthens earlier results concerning linear homeomorphisms. The second example is a non-Lindelöf function space Cp(X), whereX is a monolithic perfectly normal compact spa...

In this article, we studied the convergence of regional economic growth in Beijing. We divided 18 districts and counties in Beijing into four economic regions, utilized the method of Gini coefficient decomposition to educe the σ -convergence didn’t exist in the regional economic growth of Beijing. At the same time, we utilized the panel data model and the spatial panel data model analysis to ed...

The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-regular convergence spaces is explored, with particular emphasis on the former, since they have not been p...

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

Regional convergence is one of the major goals of the European Union. In this paper, the intention is to augment the existing literature on regional convergence across the NUTS-2 regions of EU-27 in terms of agricultural labour productivity during the period 1995-2004. A low annual rate of absolute convergence is estimated for the NUTS-2 regions over the period 1995-2004. The rate of regional c...