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
In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space 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 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
Let K be a compact Hausdorff space, the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and the topology in C(K) of pointwise convergence on D. It is proved that when is Lindelöf the -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 is Lindelöf, then K is metrizable if, and only if, there is a countable and dense...
The Lindelöf property in Banach spaces
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 the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
James boundaries and σ-fragmented selectors
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 we study different kinds of conditions on T, besides T being countable, which ensure that . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if 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.
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