Generalized statistical convergence and convergence free spaces


Nuray F., Ruckle W.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.245, no.2, pp.513-527, 2000 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 245 Issue: 2
  • Publication Date: 2000
  • Doi Number: 10.1006/jmaa.2000.6778
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.513-527

Abstract

Many results about statistical convergence in a general setting can be derived by consideration of the convergence free space of null sequences and its related cofilter and filter. We derive algebraic and order properties, preservation under uniform convergence, Cauchy properties, and properties of cluster points. We also show that for certain types of statistical convergence stronger convergence properties also hold. Finally we discuss the relationship between generalized statistical convergence and subsets of the Stone-Cech compactification of the integers. (C) 2000 Academic Press.