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

Abstract

Let  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 inverstigate I ₂ -convergence and -convergence of double sequences in a topological space and establish some basic teorems. Furthermore we introduce of I ₂ -Cauchy and -Cauchy notions for double sequences in topological groups.