Topological Modules of Bounded Bigroup Homomorphisms on a Topological Module

Abstract

Let X, Y, and Z be topological modules over a topological ring R. In this 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 the operations of addition and module multiplication are continuous for each class of bounded bigroup homomorphisms. Also, we investigate whether each class of bounded bigroup homomorphisms is uniformly complete.

arXiv comment5 pages. This paper is merged with another paper entitled as " A few remarks on boundedness in topological modules and topological groups" which is available in arXiv, with some modification