The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.

Título inglés	The algebraic dimension of linear metric spaces and Baire properties of their hyperspaces.
Título español	Dimensión algebraica de espacios métricos lineales y propiedades de Baire de sus hiperespacios.
Autor/es	Banakh, Taras ; Plichko, Anatolij
Organización	Inst. Mat. Akad. Swietokrzyska, Kielce, Polonia;Dep. Math. Ivan Franko Lviv Nat. Univ., Lviv. Ucrania;Inst. Mat. Politech. Krakowska, Cracovia, Polonia
Revista	1578-7303
Publicación	2006, 100 (1-2): 31-37, 13 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Answering a question of Halbeisen we prove (by two different methods) that the algebraic dimension of each infinite-dimensional complete linear metric space X equals the size of X. A topological method gives a bit more: the algebraic dimension of a linear metric space X equals |X| provided the hyperspace K(X) of compact subsets of X is a Baire space. Studying the interplay between Baire properties of a linear metric space X and its hyperspace, we construct a hereditarily Baire linear metric space X with meager hyperspace K(X). Also under (d = c) we construct a metrizable separable noncomplete linear metric space with hereditarily Baire hyperspace. We do not know if such a space can be constructed in ZFC.
Código MathReviews	MR2267398
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