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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasi-continuité, continuité séparées, et topologie extrémale


Author: Jean-Pierre Troallic
Journal: Proc. Amer. Math. Soc. 110 (1990), 819-827
MSC: Primary 54C05; Secondary 46B20, 46G99, 54E52
MathSciNet review: 993759
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Abstract: Let $ E$ be a Banach space, $ {X_1}, \ldots ,{X_n}$ strongly countably complete regular spaces and $ \Phi :{X_1} \times \cdots \times {X_n} \to E$ a function. We prove, particularly by means of techniques borrowed from J. P. R. Christensen, that if $ \Phi $ is separately continuous and quasi-continuous when $ E$ is equipped with the extremal topology, then $ \Phi $ is jointly continuous at each point of a dense $ {G_\delta }$ subset of $ {X_1} \times \cdots \times {X_n}$ when $ E$ is equipped with the norm topology. Various properties--new or already known--are obtained by using this result.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0993759-X
PII: S 0002-9939(1990)0993759-X
Keywords: Separate and joint continuity, quasicontinuity, extremal topology on a Banach space
Article copyright: © Copyright 1990 American Mathematical Society