The Lindelöf property and σ-fragmentability

• Autorzy: B. Cascales , I. Namioka
• Języki publikacji: EN

Abstrakty

EN

In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space $[-1,1]^{D}$ is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of $[-1,1]^{D}$ is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then $(X,γ(D))^{ℕ}$ is also Lindelöf. We give several applications of this theorem in areas of topology and Banach spaces. We also show by examples that the main theorem cannot be extended to the cases where X is Čech-analytic and Lindelöf or countably K-determined.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 54C35: Function spaces
• 46A50: Compactness in topological linear spaces; angelic spaces, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 180
• Numer: 2
• Strony: 161-183

Daty

wydano

2003

Twórcy

autor

B. Cascales

• Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain

autor

I. Namioka

• University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195-4350, U.S.A.

Identyfikatory

DOI

10.4064/fm180-2-3