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His health was poor for long spells and, after writing his thesis, he was only able to contribute to mathematics for a few short spells. In 1902 Baire was appointed to the University of Montpellier and in 1905 to Dijon.
He wrote important analysis books including Théorie des nombres irrationels, des limites et de la continuité (1905) and Lecons sur les théories générales de l'analyse , 2 Vols. (1907-8).
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