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Continuous images and other topological properties of Valdivia compacta

100%

Kalenda O.

Fundamenta Mathematicae

1999

tom 162

nr 2

181-192

We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.

Valdivia compacta and equivalent norms

100%

Kalenda O.

Studia Mathematica

2000

tom 138

nr 2

179-191

We prove that the dual unit ball of a Banach space X is a Corson compactum provided that the dual unit ball with respect to every equivalent norm on X is a Valdivia compactum. As a corollary we show that the dual unit ball of a Banach space X of density $ℵ_1$ is Corson if (and only if) X has a projectional resolution of the identity with respect to every equivalent norm. These results answer questions asked by M. Fabian, G. Godefroy and V. Zizler and yield a converse to Amir-Lindenstrauss' theorem.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Kalenda O.

1 2000

1 1999

Wyniki wyszukiwania

Continuous images and other topological properties of Valdivia compacta

Valdivia compacta and equivalent norms