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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 ,
we show that is Corson if and only
if every continuous image...
We show that an infinite-dimensional complete linear space X has:
∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺;
∙ a dense non-meager Hamel basis if for some cardinal κ.
We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal.
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