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Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first...

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 * = s p a n T ¯ | | · | | . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if J : X → 2 B X * is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...

Les espaces de Berkovich sont angéliques

Jérôme Poineau (2013)

Bulletin de la Société Mathématique de France

Bien que les espaces de Berkovich définis sur un corps trop gros ne soient, en général, pas métrisables, nous montrons que leur topologie reste en grande partie gouvernée par les suites : tout point adhérent à une partie est limite d’une suite de points de cette partie et les parties compactes sont séquentiellement compactes. Notre preuve utilise de façon essentielle l’extension des scalaires et nous en étudions certaines propriétés. Nous montrons qu’un point d’un disque peut être défini sur un...

Mazur spaces.

Wilansky, Albert (1981)

International Journal of Mathematics and Mathematical Sciences

Metrizability of precompact sets: an elementary proof.

J. C. Ferrando, J. Kakol, M. López Pellicer (2005)

RACSAM

Proporcionamos una demostración muy corta de un teorema de Cascales-Orihuela que establece que todo conjunto precompacto de un espacio localmente convexo de la clase G (en el sentido de Cascales-Orihuela) es metrizable.

On complete, precompact and compact sets.

Leonhard Frerick (1993)

Collectanea Mathematica

Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.

On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski (1995)

Studia Mathematica

We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.

Currently displaying 41 – 60 of 107