Listar GI-GMNE - Artigos por autor "Domínguez, Xabier"

Mostrando ítems 1-7 de 7

    • Krein’s theorem in the context of topological abelian groups 

      Borsich, Tayomara; Domínguez, Xabier; Martín Peinador, Elena (MDPI, 2022)
      [Abstract:] A topological abelian group G is said to have the quasi-convex compactness property (briefly, qcp) if the quasi-convex hull of every compact subset of G is again compact. In this paper we prove that there exist ...

    • On g-barrelled groups and their permanence properties 

      Borsich, Tayomara; Chasco, MJ; Domínguez, Xabier; Martín Peinador, Elena (Elsevier, 2019)
      [Abstract:] The g-barrelled groups constitute a vast class of abelian topological groups. It might be considered as a natural extension of the class of barrelled topological vector spaces. In this paper we prove that ...

    • On local cross sections in topological abelian groups 

      Bello, Hugo J.; Chasco, MJ; Domínguez, Xabier; Stevens, T. Christine (Springer, 2018)
      [Abstract:] We introduce the notion of local pseudo-homomorphism between two topological abelian groups. We prove that it is closely related with the widely studied notions of local cross sections and splitting extensions ...

    • On Local Quasi-Convexity as a Three-Space Property in Topological Abelian Groups 

      Domínguez, Xabier; Tarieladze, Vaja (Elsevier, 2021)
      [Abstract] Let X be a topological abelian group and H a subgroup of X. We find conditions under which local quasi-convexity of both H and results in the same property for X. This is true for instance if H is precompact, ...

    • On the existence of topologies compatible with a group duality with predetermined properties 

      Borsich, Tayomara; Domínguez, Xabier; Martín Peinador, Elena (Elsevier, 2022)
      [Abstract:] The paper deals with group dualities. A group duality is simply a pair (G, H) where G is an abstract abelian group and H a subgroup of characters defined on G. A group topology τ defined on G is compatible with ...

    • Permutations, Signs, and Sum Ranges 

      Chobanyan, Sergei; Domínguez, Xabier; Tarieladze, Vaja; Vidal, Ricardo (MDPI, 2023)
      [Abstract:] The sum range SR[x; X], for a sequence x = (xn)n∈N of elements of a topological vector space X, is defined as the set of all elements s ∈ X for which there exists a bijection (=permutation) π : N → N, such that ...

    • Topological Groups of Lipschitz Functions and Graev Metrics 

      Chasco, MJ; Domínguez, Xabier; Tkachenko, Mikhail (Elsevier, 2022)
      [Abstract] We study the properties of the free abelian topological group Ad(X) on a metric space (X,d) endowed with the topology generated by the Graev extension dˆ of a given metric d on X. We find that the group of ...