  We prove that a countably compact space is monotonically retractable if and
only if it has a full retractional skeleton. In particular, a compact space is
monotonically retractable if and only if it is Corson. This gives an answer to
a question of R. Rojas-Hern{\'a}ndez and V. V. Tkachuk. Further, we apply this
result to characterize retractional skeleton using a topology on the space of
continuous functions, answering thus a question of the first author and a
related question of W. Kubi\'s.
