Some topological properties of the set of filter cluster functions


ALBAYRAK H. , PEHLİVAN S. , MOHAPATRA R. N.

KUWAIT JOURNAL OF SCIENCE, cilt.43, sa.3, ss.78-85, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Konu: 3
  • Basım Tarihi: 2016
  • Dergi Adı: KUWAIT JOURNAL OF SCIENCE
  • Sayfa Sayıları: ss.78-85

Özet

In Albayrak & Pehlivan (2013), we generalized the concepts of pointwise convergence, uniform convergence and alpha-convergence for sequences of functions on metric spaces by using the filters on N. In this work, we define the concepts of limit function, F-limit function and F-cluster function respectively for each of these three types of convergence, where F is a filter on N. We investigate some topological properties of the sets of F-pointwise cluster functions, F-alpha-cluster functions and F-uniform cluster functions by using pointwise and uniform convergence topologies.