IKIK-Cauchy functions

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