2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135174We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. Especially, we show that such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. From the dimension formula for affine Deligne-Lusztig varieties we obtain a description of the set of these varieties that are zero-dimensional.15 pages, some errors corrected, to appear in Mathematische AnnalenAlgebraic Geometry20G25, 14G35text