I~κ-Cauchy functions

摘要

In this paper we introduce the notion of I~κ-Cauchy function, where I and κ are ideals on the same set. The I~κ-Cauchy functions are a generalization of I~*-Cauchy sequences and I~*-Cauchy nets. We show how this notion can be used to characterize complete uniform spaces and we study how I~κ-Cauchy functions and I-Cauchy functions are related. We also define and study I~κ-divergence of functions.