A few remarks on boundedness in topological modules and topological groups

Authors : Omid Zabeti

Pages : 420-426

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Publication Date : 2019-04-01

Article Type : Research

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.
Keywords : Bigroup homomorphism, topological module, boundedness, topological group