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

Abstract

In this paper, we first define an equivalence relation on the sequence space $\Sigma _{2}$. Then we equip the quotient set $\Sigma _{2}/_{\sim}$ with a metric $d_1$. We also determine an isometry map between the metric spaces $(\Sigma _{2}/_{\sim},d_1)$ and $([0,1],d_{eucl})$. Finally, we investigate the symmetry conditions with respect to some points on the metric space $(\Sigma _{2}/_{\sim},d_1)$ and we compare truncation errors for the computations which is obtained by the metrics $d_{eucl}$ and $d_1$.