2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142463We pursue the study of the multiscale spaces $S^ν$ introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for $S^ν$ to be locally p-convex, and exhibit a sequence of $p$-norms that defines its natural topology. The strong topological dual of $S^ν$ is identified to another sequence space depending on $ν$, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces.30 pages, 2 figures. To appear in J. Math. Anal. ApplFunctional AnalysisGeneral TopologyMetric Geometry46A45 (Primary) 46A16, 46A20 (Secondary)text