- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 2
- A few remarks on boundedness in topological modules and topological groups
A few remarks on boundedness in topological modules and topological groups
Authors : Omid Zabeti
Pages : 420-426
View : 11 | Download : 6
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