Author: George Galanis
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  • University of Athens Department of Mathematics Panepistimiopolis 15784 Athens Greece
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In this paper we characterize commutative Fréchet-Lie groups using the exponential map. In particular we prove that if a commutative Fréchet-Lie groupG has an exponential map, which is a local diffeomorphism, thenG is the limit of a projective system of Banach-Lie groups.