In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a nonempty set. Also we have used the idea of $I$-convergence of double sequences to study the idea of $I$-sequential compactness in the sense of double sequences [A.K. Banerjee, A. Banerjee, A note on $I$-convergence and $I^{*}$-convergence of sequences and nets in a topological space, Mat. Vesnik 67, 3 (2015), 212-221].