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FONCTIONS SÉPARÉMENT CONTINUES ET DE PREMIÈRE CLASSE SUR UN ESPACE PRODUIT

GABRIEL DEBS
Mathematica Scandinavica
Vol. 59 (1986), pp. 122-130
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24491829
Page Count: 9
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FONCTIONS SÉPARÉMENT CONTINUES ET DE PREMIÈRE CLASSE SUR UN ESPACE PRODUIT
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Abstract

We prove that if X = Y = [0, 1] and f: X × Y → R is continuous in one of the two variables and of the first Baire class in the other variable, then f is jointly continuous at any point of a dense Gδ subset of X × Y. The result is proved under quite general assumptions on X and Y, in particular when X and Y are metrizable spaces such that the product space X × Y is a Baire space. On montre que si X = Y = [0, 1] et f: X × Y → R est continue en l'une des variables et de première classe de Baire en l'autre, alors f est continue en tout point d'un résiduel de X × Y. En fait le résultat est démontré sous des hypothèses assez générales sur X et Y, en particulier lorsque X et Y sont des espaces métrisables dont le produit X × Y est un espace de Baire.

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