Abstract 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]. 
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