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Nous donnons dans ce travail une caractérisation des algèbres (semi-simples) localement-convexes complètes faiblement topologisées au sens de S. Warner, ce qui clarifie, entre autres, plusiers résultats données sur certaines classes d'algèbres à base étudiées par de nombreux auteurs ([2], [6], [7]) pour approcher le problème de E. A. Michael sur la continuité des caractères dans les algèbres de Fréchet [9].
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