  We prove some generalizations of results concerning Valdivia compact spaces
(equivalently spaces with a commutative retractional skeleton) to the spaces
with a retractional skeleton (not necessarily commutative). Namely, we show
that the dual unit ball of a Banach space is Corson provided the dual unit ball
of every equivalent norm has a retractional skeleton. Another result to be
mentioned is the following. Having a compact space K, we show that K is Corson
if and only if every continuous image of K has a retractional skeleton.
