Quasi-continuité, continuité séparées, et topologie extrémale
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- by Jean-Pierre Troallic PDF
- Proc. Amer. Math. Soc. 110 (1990), 819-827 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 819-827
- MSC: Primary 54C05; Secondary 46B20, 46G99, 54E52
- DOI: https://doi.org/10.1090/S0002-9939-1990-0993759-X
- MathSciNet review: 993759