On I-Cauchy nets and completeness

In this paper we extend the idea of usual Cauchy condition of nets to I-Cauchy condition by using the concept of ideals. This Cauchy condition arises naturally from the notion of I-convergence of nets introduced by Lahiri and Das (2008). As the underlying structure for the whole study we take a uniform space so that our notion and results extend the idea of statistical Cauchy sequences very recently introduced in uniform spaces by Di Maio and Kočinac (2008). In particular we try to give partial answers to an open problem posed by Di Maio and Kočinac and examine the relationship between this new Cauchy condition and usual completeness of a uniform space.