  We 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.
