Topological Modules of Bounded Bigroup Homomorphisms on a Topological\n Module

2014/09/25 by Omid Zabeti, Zabeti, Omid
Decision Sciences · Mathematics · #13J99 #16W80 #54H13 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1409.7363

openalex publication_date 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X, Y, and Z be topological modules over a topological ring R. In this\npaper, we introduce three different classes of bounded bigroup homomorphisms\nfrom X \× Y into Z with respect to the three different uniform convergence\ntopologies. We show that the operations of addition and module multiplication\nare continuous for each class of bounded bigroup homomorphisms. Also, we\ninvestigate whether each class of bounded bigroup homomorphisms is uniformly\ncomplete.\n

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