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Noncommutative Valdivia compacta

Marek Cúth (2014)

Commentationes Mathematicae Universitatis Carolinae

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...

Normal Vietoris implies compactness: a short proof

G. Di Maio, E. Meccariello, Somashekhar Naimpally (2004)

Czechoslovak Mathematical Journal

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.

Note on countable unions of Corson countably compact spaces

Ondřej F. K. Kalenda (2004)

Commentationes Mathematicae Universitatis Carolinae

We show that a compact space K has a dense set of G δ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in K , then K is even Corson.

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