Lk-Cauchy functions

In this paper we introduce the notion of I K -Cauchy function, where I and K are ideals on the same set. The I K -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 K -Cauchy functions and I -Cauchy functions are related. We also define and study I K -divergence of functions.