Displaying similar documents to “Embedding a topological group into its WAP-compactification”

A new class of weakly countably determined Banach spaces

K. K. Kampoukos, S. K. Mercourakis (2010)

Fundamenta Mathematicae

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A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.

A theorem of the Hahn-Banach type and its applications

Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor (1992)

Annales Polonici Mathematici

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Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.