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Espaces К-analytiques et espaces de Baire de fonctions continues

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  26 February 2010

Gabriel Debs
Gabriel Debs
Affiliation:
Équipe D'Analyse, Université Paris VI, 4, Place Jussieu, 75230 Paris Cedex 05, France.
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Extract

Le point de départ de ce travail est le résultat suivant.

THÉORÈME (I. Namioka). Soient X et Y deux espaces compacts et

Si f est continue quand on munit(Y) de la topologie de convergence simple alors X contient un Gδ dense en tout point duquel f reste continue quand on munit(Y) de la topologie de la convergence uniform.

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Mathematika , Volume 32 , Issue 2 , December 1985 , pp. 218 - 228
Copyright
Copyright © University College London 1985

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References

1.Calbrix, J. et Troallic, J. P.. Applications separement continues. C.R. Acad. Sci. Paris, 288 (1979), 647–648.Google Scholar
2.Choquet, G.. Lectures on Analysis, Vol. 1 (W. A. Benjamin Inc., New-York, Amsterdam, 1969).Google Scholar
3.Christensen, J. P. R.. Joint continuity of separately continuous functions. Proc. Amer. Math. Soc., 82 (1981), 455–461.CrossRefGoogle Scholar
4.Christensen, J. P. R.. 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.CrossRefGoogle Scholar
5.Christensen, J. P. R.Theorems of Namioka and Johnson type for u.s.c.o. set-valued mappings. Proc. Amer. Math. Soc, 86 (1982), 649–655.CrossRefGoogle Scholar
6.Deville, R.. Parties faiblement de Baire dans les espaces de Banach. ThèseUniversité Paris VI.Google Scholar
7.Namioka, I.. Separate and joint continuity. Pacific J. of Math., 51 (1974), 515–531.CrossRefGoogle Scholar
8.Saint-Raymond, J.. Jeux topologiques et espaces de Namioka. Proc. Amer. Math. Soc, 87 (1983), 499–504.CrossRefGoogle Scholar
9.Stegall, C.. Gateaux differentiation of functions on a certain class of Banach spaces. Functional Analysis: Surveys and Recent Results III (Elsevier Science Publishers, North-Holland, 1984).Google Scholar
10.Talagrand, M.. Deux généralisations d'un théorème de I. Namioka. Pacific J. Math., 81 (1979), 239–251.CrossRefGoogle Scholar
11.Talagrand, M.. Espace de Baire et espaces de Namioka. Math. Annalen, 270 (1985), 159–164.CrossRefGoogle Scholar