EUDML

The search session has expired. Please query the service again.

Currently displaying 1 – 8 of 8

Order by Relevance | Title | Year of publication

Countably determined locally convex spaces

Cascales, B.; Orihuela, J. — 1991

Portugaliae mathematica

Estructuras ordenadas relacionadas con el teorema de la gráfica cerrada.

B. Cascales — 1986

Collectanea Mathematica

On Compactness in Locally Convex Spaces.

B. Cascales; J. Orihuela — 1987

Mathematische Zeitschrift

The Lindelöf property and σ-fragmentability

B. Cascales; I. Namioka — 2003

Fundamenta Mathematicae

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...

Fragmentability and compactness in C(K)-spaces

B. Cascales; G. Manjabacas; G. Vera — 1998

Studia Mathematica

Let K be a compact Hausdorff space, $C_{p} (K)$ the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and $t_{p} (D)$ the topology in C(K) of pointwise convergence on D. It is proved that when $C_{p} (K)$ is Lindelöf the $t_{p} (D)$ -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and $C_{p} (K)$ is Lindelöf, then K is metrizable if, and only if, there is a countable and dense...

The Lindelöf property in Banach spaces

B. Cascales; I. Namioka; J. Orihuela — 2003

Studia Mathematica

A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space $M^{D}$ the following four conditions are equivalent: (i) K is fragmented by $d_{D}$ , where, for each S ⊂ D, $d_{S} (x, y) = s u p ϱ (x (t), y (t)) : t \in S$ . (ii) For each countable subset A of D, $(K, d_{A})$ is...

James boundaries and σ-fragmented selectors

B. Cascales; M. Muñoz; J. Orihuela — 2008

Studia Mathematica

We study the boundary structure for w*-compact subsets of dual Banach spaces. To be more precise, for a Banach space X, 0 < ϵ < 1 and a subset T of the dual space X* such that ⋃ B(t,ϵ): t ∈ T contains a James boundary for $B_{X *}$ we study different kinds of conditions on T, besides T being countable, which ensure that $X * = {\bar{s p a n T}}^{| | \cdot | |}$ . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if $J : X \to 2^{B_{X *}}$ is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...

La propiedad de Radon-Nikodym en espacios de Banach duales.

B. Cascales; A. J. Pallarés — 1994

Collectanea Mathematica

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 8 of 8

Countably determined locally convex spaces

Estructuras ordenadas relacionadas con el teorema de la gráfica cerrada.

On Compactness in Locally Convex Spaces.

The Lindelöf property and σ-fragmentability

Fragmentability and compactness in C(K)-spaces

The Lindelöf property in Banach spaces

James boundaries and σ-fragmented selectors

La propiedad de Radon-Nikodym en espacios de Banach duales.