ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Research article
On the joint continuity of module multiplication; pp. 6–16
PDF | https://doi.org/10.3176/proc.2023.1.02

Author
Mart Abel
Abstract

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. 

References

1. Balachandran, V. K. Topological Algebras. Reprint of the 1999 original. North-Holland Mathematics Studies, Vol. 185. North- Holland Publishing Co., Amsterdam, 2000. 

2. Haralampidou, M., Oudadess, M., Palacios, L. and Signoret, C. On locally A-convex modules. Mediterr. J. Math., 2022, 19(1), 23. 
https://doi.org/10.1007/s00009-021-01935-x

3. Köthe, G. Topological Vector Spaces I. Die Grundlehren der mathematischen Wissenschaften, Vol. 159. Springer, Berlin, Heidelberg, New York, 1969. 

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