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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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 $d_1$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we first define an equivalence relation on the sequence space $\Sigma _{2}$.
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Key Findings & Data:Then we equip the quotient set $\Sigma _{2}/_{\sim}$ with a metric $d_1$.
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Conclusion & Impact: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 $d_1$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Metric spaces · symbolic dynamics · isometry
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 $d_1$.
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Cite This Article
SALTAN, M., ASLAN, N. (2021). A metric formula on a quotient space which is related to the sequence space $\Sigma _{2}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 1, 320–330. https://ajindex.com/articles/746750