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Feechet-Urysohn (briefly F-U) property for topological spaces is known to be highly non-multiplicative: for instance, the square of a compact F-U space is not in general Frechet-Urysohn [P. Simon, A compact Frechet space whose square is not Frec[...]texto impreso
For a normed infinite-dimensional space, we prove that the family of all locally convex topologies which are compatible with the original norm topology has cardinality greater or equal to c.texto impreso
Bruguera Padró, M. Montserrat ; Chasco, M.J. ; Martín Peinador, Elena ; Tarieladze, Vaja | Elsevier Science | 2000-04-16It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, i[...]texto impreso
We study various degrees of completeness for a Tychonoff space X. One of them plays a central role, namely X is called a Conway space if X is sequentially closed in its Stone–?ech compactification ? X (a prominent example of Conway spaces is pro[...]texto impreso
We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X [...]texto impreso
Bruguera Padró, M. Montserrat ; Martín Peinador, Elena ; Tarieladze, Vaja | Oxford University Press | 2004Leaning on a remarkable paper of Pryce, the paper studies two independent classes of topological Abelian groups which are strictly angelic when endowed with their Bohr topology. Some extensions are given of the Eberlein–?Smulyan theorem for the [...]texto impreso
For a topological abelian group X we topologize the group c0(X) of all X-valued null sequences in a way such that when X= the topology of c0() coincides with the usual Banach space topology of the classical Banach space c0. If X is a non-trivial[...]texto impreso
K?kol, Jerzy ; López Pellicer, Manuel ; Martín Peinador, Elena ; Tarieladze, Vaja | WALTER DE GRUYTER | 2008Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and sigma-compact. (ii) C-p(X) is analytic. (iii) C-p(X) is K-analytic. (iv) C-p(X) is Lindelof. (v) [...]texto impreso
Martín Peinador, Elena ; Chasco, M.J. ; Tarieladze, Vaja | Polish Acad Sciencies Inst Mathematics | 1999The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is n[...]texto impreso
The property of Dunford-Pettis for a locally convex space was introduced by Grothendieck in 1953. Since then it has been intensively studied, with especial emphasis in the framework of Banach space theory. In this paper we define the Bohr sequen[...]
