Preservation of the Borel class under countable-compact-covering mappings |
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Authors: | Jean Saint Raymond |
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Institution: | Analyse Fonctionnelle, Institut de Mathématique de Jussieu, Boîte 186, 4, place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | The aim of this note is to prove the following result: “Assume that X is a metric Borel space of class ξ, that is continuous, that every fiber f−1(y) is complete and that every countable compact subset of Y is the image by f of some compact subset of X. Then Y is Borel and moreover of class ξ”. We give also an extension to the case where the fibers are only assumed to be Polish. |
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Keywords: | primary 03E15 secondary 03E45 54H05 |
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