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

A few remarks on boundedness in topological modules and topological groups

Omid Zabeti
Sayfa
420–426
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez:Let $X$, $Y$, and $Z$ be topological modules over a topological ring $R$.
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Temel Bulgular & Veri: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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Sonuç & Katkı:In the second part, we characterize bounded sets in the arbitrary product of topological groups with respect to the both product and box topologies.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (8)

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  8. O. Zabeti and Lj.D.R. Kocinac, A few remarks on bounded operators on topological vector spaces, Filomat, 30 (3), 763–772, 2016.