The set of filter cluster functions

Abstract

In this work, we are concerned with the concepts of F-α-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.