On I-concurrent class of sequences

Abstract

In this paper, we demonstrate the $\mathcal{I}$-concurrent relation between sequences and the equivalence relations produced from it. A few unique features of these equivalence classes are investigated. Finally, we show that the collection of all such equivalence classes of all $\mathcal{I}$-convergent sequences under the $\mathcal{I}$-concurrent relation generates a metric space that is isometric with the set of all constant sequences.