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

Abstract

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 ${\mathcal{I}}^{\ast }$-Cauchy sequences and ${\mathcal{I}}^{\ast }$-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.

Cited by in corpus (2)

• Further aspects of ${\mathcal{I}}^{\mathcal{K}}$-convergence in Topological Spaces
• On $I^K$-Convergence in a Topological space via semi-open sets