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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Additionally, we establish that both of the spaces $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ include the space $\mathcal{BS}$ of bounded double series.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ denote the spaces of almost null and almost convergent double sequences, respectively.
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Key Findings & Data:We show that $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ are BDK-spaces, barreled and bornological, but they are not monotone and so not solid.
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Conclusion & Impact:Additionally, we establish that both of the spaces $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ include the space $\mathcal{BS}$ of bounded double series.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Double sequence · Pringsheim convergence · almost convergence
Abstract
Let $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ denote the spaces of almost null and almost convergent double sequences, respectively. We show that $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ are BDK-spaces, barreled and bornological, but they are not monotone and so not solid. Additionally, we establish that both of the spaces $\mathcal{C}_{f_0}$ and $\mathcal{C}_{f}$ include the space $\mathcal{BS}$ of bounded double series.
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Cite This Article
YEŞİLKAYAGİL, M., BAŞAR, F. (2016). Some topological properties of the spaces of almost null andalmost convergent double sequences. Turkish Journal of Mathematics, Cilt: 40 - Sayı: 3, 624–630. https://ajindex.com/articles/723267