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Sequentially continuous mappings of product spaces

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Sequentially continuous mappings of product spaces Séminaire d’analyse fonctionnelle École Polytechnique D. V. CHOODNOVSKY Sequentially continuousmappings of product spaces Séminaire d’analyse fonctionnelle (Polytechnique) (1977-1978), exp. no 4, p. 1-15. <http://www.numdam.org/item?id=SAF_1977-1978____A3_0> © Séminaire d’analyse fonctionnelle (École Polytechnique), 1977-1978, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation com- merciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ SEMINAIRE SUR LAG E 0 MET R I E DES ESPACES DE BANACH 1977-1978 SEQUENTIALLY CONTINUOUS MAPPINGS OF PRODUCT SPACES D. V. CHOODNOVSKY ECOLE POLYTECHNIQUE CENTRE DE MATHÉMATIQUES PLATEAU DE PALAISEAU . 91128 PALAISEAU CEDEX Téléphone : 941.82.00 - Poste No Tdlex : ECOLEX 691596 F Expose No IV 18 Novembre 1977 IV.1 § 0. INTRODUCTION It is trivial that any sequentially continous mapping between metric spaces is continuous. It is natural to pose the following question : for what classes of product of metric spaces are the sequentially continuous mappings (e.g. into metric spaces) continuous ? At first this problem in a proper way was posed in an extremely interesting paper of S. Mazur [1J. For about 20 years this paper was the most advanced in this direction. Mazur had shown that this problem can be reduced to the investigation of some special topological and set theoretical properties. After this in the classical review of Keisler and Tarski [2] the Mazur results were quoted and some concrete questions about sequentially con- tinuous mappings of 2ð -~2, 2 were given. Now we formulate these questions.

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