Propiedades (BB)n y topologías en P(nE)

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Properties (BB)n, n = 2, 3, ... on a locally convex space (see the definition below) have been recently introduced ([10]). They are interesting, among other things, in connection with the study of natural topologies on spaces of polynomials, multilinear and holomorphic mappings. As it is proved in [1] there are Fr´echet spaces with the (BB)2 property but without the (BB)3 property. Here, for a given n = 3, ... we get an space without the property (BB)n+1 and study an equivalent condition for that space to have the (BB)n property
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