  We give a new characterization of Valdivia compact spaces: A compact space is
Valdivia if and only if it has a dense commutatively monotonically retractable
subspace. This result solves Problem 5.12 from \cite{sal-rey}. Besides, we
introduce the notion of full $c$-skeleton and prove that a compact space is
Corson if and only if it has a full $c$-skeleton.
