A few remarks on boundedness in topological modules and topological groups

Omid Zabeti

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arXiv · 1611.01631

A few remarks on boundedness in topological modules and topological groups

Omid Zabeti

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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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Omid Zabeti. 2016-11-05. A few remarks on boundedness in topological modules and topological groups. https://arxiv.org/abs/1611.01631

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