  In this paper, we deal with a hyperspace selection problem in the setting of
connected spaces. We present two solutions of this problem illustrating the
difference between selections for the nonempty closed sets, and those for the
at most two-point sets. In the first case, we obtain a characterisation of
compact orderable spaces. In the latter case -- that of selections for at most
two-point sets, the same selection property is equivalent to the existence of a
ternary relation on the space, known as a cyclic order, and gives a
characterisation of the so called weakly cyclically orderable spaces.
