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Joint continuity of separately continuous
mappings on topological groups


Author: H. R. Ebrahimi-Vishki
Journal: Proc. Amer. Math. Soc. 124 (1996), 3515-3518
MSC (1991): Primary 54C05, 22A10
MathSciNet review: 1346970
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Abstract: The main theorem of this paper is somewhat stronger than the following statement: Let $G$ be a Baire semitopological group, let $H$ be a first countable one and let $N$ be a first countable topological group; then each separately continuous bi-homomorphism from $G\times H$ into $N$ is jointly continuous. This theorem has some consequences on joint continuity of separately continuous multiplication of rings and scalar multiplication of modules.


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Additional Information

H. R. Ebrahimi-Vishki
Affiliation: Department of Mathematics, Mashhad University, P. O. Box 1159, Mashhad 91775, Iran
Email: vishki@science2.um.ac.ir

DOI: https://doi.org/10.1090/S0002-9939-96-03538-1
Keywords: Separate and joint continuity, Baire space, $\sigma$-well-$\beta$-defavorable space, topological group
Received by editor(s): March 21, 1994
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society