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Keywords:
retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces
retractional skeleton; projectional skeleton; Valdivia compacta; Plichko spaces
Summary:
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. We also present
some open problems in this area.
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