A sort of strong completeness property for subsets of a non-Archimedean
space is defi{}ned. On the subsets which satisfy this property there
exists a Vietoris continuous selector. The set of discrete closed
subsets of $\mathbb{R}$ has a continuous selector when it is equipped
with the Vietoris topology induced by the Michael line. Some properties
of the tree of a non-Archimedean space are used.
