I^K-Cauchy functions

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In this paper we introduce the notion of

$\mathcal I^{\mathcal K}$ -Cauchy function, where

$\mathcal I$ and

$\mathcal K$ are ideals on the same set. The

$\mathcal I^{\mathcal K}$ -Cauchy functions are a generalization of

$\mathcal I^*$ -Cauchy sequences and

$\mathcal I^*$ -Cauchy nets. We show how this notion can be used to characterize complete uniform spaces and we study how

$\mathcal I^{\mathcal K}$ -Cauchy functions and

$\mathcal I$ -Cauchy functions are related. We also define and study

$\mathcal I^{\mathcal K}$ -divergence of functions.