A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$

Abstract

In this paper, we …rst de…ne an equivalence relation on the sequence space 2 . Then we equip the quotient set 2 = with a metric d 1 . We also determine an isometry map between the metric spaces ( 2 = ; d 1 ) and ([0; 1]; d eucl ). Finally, we investigate the symmetry conditions with respect to some points on the metric space ( 2 = ; d 1 ) and we compare truncation errors for the computations which is obtained by the metrics d eucl and d 1 .