Some remarks on Radon-Nikodym compact spaces

• Autorzy: Alexander D. Arvanitakis
• Języki publikacji: EN

Abstrakty

EN

The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon-Nikodým space which is almost totally disconnected is actually a Radon-Nikodým compact space embeddable in the space of probability measures on a scattered compact space.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 54G12: Scattered spaces
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 1
• Strony: 41-60

Daty

wydano

2002

Twórcy

autor

Alexander D. Arvanitakis

• Department of Mathematics, University of Athens, 15784 Panepistimiopolis, Athens, Greece

Identyfikatory

DOI

10.4064/fm172-1-4