The Set of Filter Cluster Functions


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ALBAYRAK H. , PEHLİVAN S.

FILOMAT, vol.32, no.9, pp.3057-3071, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 9
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1809057a
  • Title of Journal : FILOMAT
  • Page Numbers: pp.3057-3071

Abstract

In this work, we are concerned with the concepts of F-alpha-convergence, F-pointwise convergence and F-uniform convergence for sequences of functions on metric spaces, where F is a filter on N. We define the concepts of F-limit function, F-cluster function and limit function respectively for each of these three types of convergence, and obtain some results about the sets of F-cluster and F-limit functions for sequences of functions on metric spaces. We use the concept of F-exhaustiveness to characterize the relations between these points.