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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 2

A few remarks on boundedness in topological modules and topological groups

Omid Zabeti
Pages
420–426
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $X$, $Y$, and $Z$ be topological modules over a topological ring $R$.
📊
Key Findings & Data:In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies.
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Conclusion & Impact:In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bigroup homomorphism · topological module · boundedness

Abstract

Let $X$, $Y$, and $Z$ be topological modules over a topological ring $R$. In the first part of the paper, we introduce three different classes of bounded bigroup homomorphisms from $X\times Y$ into $Z$ with respect to the three different uniform convergence topologies. We show that these spaces form again topological modules over $R$. In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.

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Cite This Article

Zabeti, O. (2022). A few remarks on boundedness in topological modules and topological groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 420–426. https://ajindex.com/articles/530151

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References (8)

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