Generalized statistical convergence and convergence free spaces


Nuray F., Ruckle W.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.245, ss.513-527, 2000 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 245 Konu: 2
  • Basım Tarihi: 2000
  • Doi Numarası: 10.1006/jmaa.2000.6778
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.513-527

Özet

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.