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We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033)forbidding a certain class of naked singularities in the spherical collapse ofa scalar field. Employing techniques similar to the ones Dafermos used, weconsider extending the theorem (1) to higher dimensions, (2) by including moregeneral matter represented by a stress-energy tensor satisfying certainassumptions, and (3) by replacing the spherical geometry by a toroidal orhigher genus (locally hyperbolic) one. We show that the extension to higherdimensions and a more general topology is straightforward; on the other hand,replacing the scalar field by a more general matter content forces us to shrinkthe class of naked singularities we are able to exclude. We then show that themost common matter theories (scalar field interacting with a non-abelian gaugefield and a perfect fluid satisfying certain conditions) obey the assumptionsof our weaker theorem, and we end by commenting on the applicability of ourresults to the five-dimensional AdS scenarii considered recently in theliterature.Comment: 16 pages, no figures, typos fixe

A note on spherically symmetric naked singularities in general dimension