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

Year 2021, Volume: 70 Issue: 1, 320 - 330, 30.06.2021

Mustafa Saltan , Nisa Aslan

https://doi.org/10.31801/cfsuasmas.729550

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 $d_1$.

Keywords

Metric spaces, symbolic dynamics, isometry, symmetry, truncation errors

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