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

Authors : Mustafa SALTAN, Nisa ASLAN

Pages : 320-330

Doi:10.31801/cfsuasmas.729550

View : 20 | Download : 8

Publication Date : 2021-06-30

Article Type : Research Paper

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 $insert ignore into journalissuearticles values(\Sigma _{2}/_{\sim},d_1);$ and $insert ignore into journalissuearticles values([0,1],d_{eucl});$. Finally, we investigate the symmetry conditions with respect to some points on the metric space $insert ignore into journalissuearticles values(\Sigma _{2}/_{\sim},d_1);$ 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