I₂-convergence and I₂-cauchy double sequences in topological groups

Abstract

Let 2N×N be a family of all subsets of N×N. Following the definition of ideal convergence in a metric space by Kostyrko et al. in 2000, ideal convergence for double sequences in a metric space was introduced by Das et al. (2008). In this paper, I investigate I₂ convergence and I2-convergence of double sequences in a topological space and establish some basic teorems. Furthermore we introduce of I₂-Cauchy and I2-Cauchy notions for double sequences in topological groups.