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].

Keywords: double sequence; $d$-limit space; ${I}$-convergence; ${I}$-limit point; ${I}$-cluster point; ${I}$-sequential compactness.

MSC: 54A20, 40A35, 40A05

Pages:  144$-$152     

Volume  69 ,  Issue  2 ,  2017