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

DOI:
https://doi.org/10.1090/S0002-9939-96-03538-1

MathSciNet review:
1346970

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Abstract | References | Similar Articles | Additional Information

Abstract: The main theorem of this paper is somewhat stronger than the following statement: Let be a Baire semitopological group, let be a first countable one and let be a first countable topological group; then each separately continuous bi-homomorphism from into is jointly continuous. This theorem has some consequences on joint continuity of separately continuous multiplication of rings and scalar multiplication of modules.

**1.**J. P. R. Christensen,*Joint continuity of separately continuous functions*, Proc. Amer. Math. Soc.**82**(1981), 455--461. MR**82h:54012****2.**------,*Remarks on Namioka spaces and R. E. Johnson's theorem on the norm separability of the range of certain mappings*, Math. Scand.**52**(1983), 112--116. MR**85c:46003****3.**J. P. R. Christensen and P. Fischer,*Joint continuity of measurable biadditive mappings*, Proc. Amer. Math. Soc.**103**(1988), 1125--1128. MR**89d:43006****4.**I. Namioka,*Separate continuity and joint continuity*, Pacific J. Math.**51**(1974), 515--531. MR**51:6693****5.**J. S. Raymond,*Jeux toplogiques et spaces de Namioka*, Proc. Amer. Math. Soc.**87**(1983), 499--504. MR**83m:54060****6.**J. Calbrix et J. P. Troallic,*Applications séparément continues*, C. R. Acad. Sci. Paris, Sér. A**288**(1979), 647--648. MR**80c:54009**

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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