On the joint continuity of module multiplication; pp. 6–16

Proceedings of the Estonian Academy of Sciences

article

Mart Abel¹ 

[1]School of Digital Technologies, Tallinn University

[2]Institute of Mathematics and Statistics, University of Tartu

关键词: joint continuity of the module multiplication;    topological modules;    submodules;    completion;    unitization;    direct products and sums;    projective and inductive limits;    tensor product.;   

DOI  :  10.3176/proc.2023.1.02

学科分类：内科医学

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

Let A be any topological algebra over R or C. We show that the property of a topological left (right or two-sided) A-module to have a jointly continuous action of A is inherited by submodules, quotient modules, completion, direct products, direct sums, projective limits and injective limits. In the case of commutative topological A-bimodules, the same property is inherited by topological tensor products.

【 授权许可】

CC BY