Functional analysis and topology were born in the first two decades of the twentieth century and each has greatly influenced the other. Identifying the dual space—the space of continuous linear functionals—of a normed space played an especially important role in the formative years of functional analysis. To further this endeavor, many new kinds (weak, strong, etc.) of convergence and compactne...

A systematic study is made of spectral measures in locally convex spaces which are countably additive for the topology of uniform convergence on bounded sets, briefly, the bounded convergence topology. Even though this topology is not compatible for the duality with respect to the pointwise convergence topology it turns out, somewhat surprisingly, that the corresponding L'-spaces for the spectr...

This paper investigates whether there is convergence in Total Factor Productivity at the establishment level, to the technological frontier. We find evidence of convergence to the frontier, which suggests the existence of technological spillovers. The speed of catch-up does not appear to vary with the extent of foreign presence in the industry. But foreign multinationals do make up a significan...

The majority of the studies on regional convergence ignore the spatial characteristics of the problem. In a recent paper Rey and Montouri (1999) considered the issue of income regional convergence on US under the spatial econometric perspective. The present paper follows the Rey and Montouri’s (1999) approach and introduces some spatial econometric techniques for convergence among Brazilian sta...

A stochastic model is presented, based on a double process of temporal drift and random disturbance, to fit the evolution of cross-country distribution of income and economic activity. Instead of assuming a steady state as is standard practice, a long run stationary equilibrium distribution is hypothesized, around which economic activity fluctuates. An empirical application comparing dynamics o...

The purpose of this article is to propose a unified theory for topologies on the closed subsets of a metrizable space. It can be shown that all of the standard hyperspace topologies—including the Hausdorff metric topology, the Vietoris topology, the Attouch-Wets topology, the Fell topology, the locally finite topology, and the topology of Mosco convergence—arise as weak topologies generated by ...

The aim of the present paper is to consider geometric properties such as starlikeness and convexity of the Cesáro partial sums of certain analytic functions in the open unit disk. By using the Cesáro partial sums, we improve some recent results including the radius of convexity. 1 Introduction Let U := {z : |z| < } be a unit disk in the complex plane C and let H denote the space of all analyti...

This paper examines the pattern of convergence in labour productivity across regions due to their ability to adopt technology. Whether regions exhibit a pattern of convergence depends on the degree to which infrastructure conditions are appropriate for the adoption of technological improvements. The ability of a region to adopt or create technology is reflected in the percentage of its labour f...

The increasing disparities between European regions constitute a great challenge for sustainable development and require identification of the factors responsible this process. Given substantive role R&amp;D in shaping innovativeness economic development, understanding its dynamics spatial patterns can provide new insights into regional growth prospects. Although prior studies have investigated...