We show that if X is a Σ 1 separable metrizable space which is not σ-compact then C p (X), the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π 1 -complete. Assuming projective determinacy we show that if X is projective not σ-compact and n is least such that X is Σ1n then Cp(X), the space of real-valued continuous functions on X with...

We remark that the result presented here can be proved more simply using the closed graph theorem. However we believe that our results can be used to prove a more interesting result. Details to follow in a later paper. One of the remarkable features of the space of holomorphic functions (in either one or several variables) is that the standard Frechet space topologies— say, for example, the L o...

The paper sets up a two-region endogenous growth model to discuss growth and regional convergence of uni ed Germany. It emphasises the role of private and public capital accumulation during the developing process. The theoretical part derives scal policy rules which establish convergence of regional output per capital and convergence of regional human wealth. To assess the speed of convergence ...

This study examines the role of tourism development in reducing regional income inequality in China. First, the theoretical foundation for how tourism affects regional income inequality is discussed. Second, based on the conditional convergence framework, this study proposes a spatiotemporal autoregressive model to capture spatial and temporal dependence as well as spatial heterogeneity. Touris...

In this study, we analyze the development experience of eco-tourism in different regions of china to find the common regional convergence which is checked with ADF test and co-integration relations. In our results, we could contribute as theoretical foundation for regional development of ecotourism in China. Meanwhile, the research result of convergence of regional eco-agricultural tourism in C...

Employing the new regression tests for Convergence, Club Convergence and Clustering proposed by Phillips and Sul (2007), this paper models and analyzes the behavior of China‘s energy sectors. Energy market ̳convergence clusters‘ are identified using new price data and their regional spatial distributions are mapped for four major fuel types; coal, gasoline, diesel and electricity. It is found t...

historically, central asia and the caucasus has been the source of important developments in the regional and global level. the whole geopolitical theories in the 20th and 21st century paid special attention to this area. geopolitical status of the region has posed challenges for residents and even neighbors of the region. these challenges can be described as the divergence factors. therefore, ...