A note on convergence of double sequences in a topological space

Abstract

In this paper we have shown that a double sequencein a topological space satisfies certain conditions which in turnare capable to generate a topology on a nonempty set. Also wehave used the idea of $I$-convergence of double sequences to studythe idea of $I$-sequential compactness in the sense of doublesequences [A.K. Banerjee, A. Banerjee, A note on $I$-convergenceand $I^{\ast }$-convergence of sequences and nets in a topologicalspace, Mat. Vesnik 67, 3 (2015), 212–221].