Nuestros investigadores

María Jesús Chasco Ugarte

Departamento
Física y Matemática Aplicada
Facultad de Ciencias. Universidad de Navarra
Líneas de investigación
Grupos topológicos. Dualidad.

Publicaciones científicas más recientes (desde 2010)

Autores: Borsich, T.; Chasco, María Jesús; Domínguez, X.; et al.
Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN 0022-247X  Vol. 473  Nº 2  2019  págs. 1203 - 1214
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 g-barrelledness is a multiplicative property, thus we obtain new examples of g-barrelled groups. We also prove that direct sums and inductive limits of g-barrelled locally quasi-convex groups are g-barrelled, too. Other permanence properties are considered as well.
Autores: Bello, H. J.; Chasco, María Jesús; Domínguez, X., (Autor de correspondencia); et al.
Revista: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
ISSN 1578-7303  2018  págs. 1 - 10
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 in the category of topological abelian groups. In the final section we present an example of a non-splitting extension of (R¿,¿¿) by R¿, where ¿¿ is a metrizable group topology on R¿ weaker than the usual one. This extension admits a local cross section.
Autores: Bejines, C., (Autor de correspondencia); Chasco, María Jesús; Elorza, Jorge; et al.
Revista: LECTURE NOTES IN COMPUTER SCIENCE
ISSN 1611-3349  Vol. 11160  2018  págs. 143 - 153
We compare four equivalence relations defined in fuzzy subgroups: Isomorphism, fuzzy isomorphism and two equivalence relations defined using level subset notion. We study if the image of two equivalent fuzzy subgroups through aggregation functions is a fuzzy subgroup, when it belongs to the same class of equivalence and if the supreme property is preserved in the class of equivalence and through aggregation functions.
Autores: Ardanza-Trevijano, Sergio; Chasco, María Jesús; Elorza, Jorge, (Autor de correspondencia)
Revista: FUZZY SETS AND SYSTEMS
ISSN 0165-0114  Vol. 369  2018  págs. 122 - 131
We implement the notion of annihilator into fuzzy subgroups of an abelian group. There are different uses for the term annihilator in algebraic contexts that have been used fuzzy systems. In this paper we refer to another type of annihilator which is essential in classical duality theory and extends the widely applied notion of orthogonal complement in Euclidean spaces. We find that in the natural algebraic duality of a group, a fuzzy subgroup can be recovered after taking the inverse annihilator of its annihilator. We also study the behavior of annihilators with respect to unions and intersections. Some illustrative examples of annihilators of fuzzy subgroups are shown, both with finite and infinite rank.
Autores: Chasco, María Jesús; Dominguez, X. ; Tkachenko, M.;
Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN 0022-247X  Vol. 448  Nº 2  2017  págs. 968 - 981
Let G be a precompact, bounded torsion abelian group and G(p)<^>, its dual group endowed with the topology of pointwise convergence. We prove that if G is Baire (resp., pseudocompact), then all compact (resp., countably compact) subsets of G(p)<^> are finite. We also prove that G is pseudocompact if and only if all countable subgroups of G(p)<^> are closed. We present other characterizations of pseudocompactness and the Baire property of G(p)<^> in terms of properties that express in different ways the abundance of continuous characters of G. Besides, we give an example of a precompact boolean group G with the Baire property such that the dual group G(p)<^> contains an infinite countably compact subspace without isolated points. (C) 2016 Elsevier Inc. All rights reserved.
Autores: Chasco, María Jesús; Dominguez, X.;
Revista: TOPOLOGY AND ITS APPLICATIONS
ISSN 0166-8641  Vol. 228  2017  págs. 285 - 293
We say that a mapping w between two topological abelian groups G and H is a pseudo-homomorphism if the associated map (x, y) is an element of G x G (bar right arrow) w(x y) -w(x) -w(y) is an element of H is continuous. This notion appears naturally in connection with cross sections (continuous right inverses for quotient mappings): given an algebraically splitting, closed subgroup H of a topological group X such that the projection pi : X -> X/H admits a cross section, one obtains a pseudo-homomorphism of X/H to H, and conversely. We show that H splits as a topological subgroup if and only if the corresponding pseudo-homomorphism can be decomposed as a sum of a homomorphism and a continuous mapping. We also prove that pseudo-homomorphisms between Polish groups satisfy the closed graph theorem. Several examples are given. (c) 2017 Elsevier B.V. All rights reserved.
Autores: Chasco, María Jesús; Domínguez, X. ; et al.
Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN 0022-247X  Vol. 435  Nº 2  2016  págs. 1607 - 1622
This paper deals with the splitting of extensions of topological abelian groups. Given topological abelian groups G and H, we say that Ext(G,H) is trivial if every extension of topological abelian groups of the form 1¿H¿X¿G¿1 splits. We prove that Ext(A(Y),K) is trivial for any free abelian topological group A(Y) over a zero-dimensional k¿-space Y and every compact abelian group K. Moreover we show that if K is a compact subgroup of a topological abelian group X such that the quotient group X/K is a zero-dimensional k¿-space, then there exists a continuous cross section from X/K to X. In the second part of the article we prove that Ext(G,H) is trivial whenever G is a product of locally precompact abelian groups and H has the form T¿×Rß for arbitrary cardinal numbers ¿ and ß. An analogous result is true if G=¿i¿IGi where each Gi is a dense subgroup of a maximally almost periodic, ¿ech-complete group for which both Ext(Gi,R) and Ext(Gi,T) are trivial.
Autores: Chasco, María Jesús;
Revista: TOPOLOGY AND ITS APPLICATIONS
ISSN 0166-8641  Vol. 185 - 186  2015  págs. 33 - 40
It is proved that, for a wide class of topological abelian groups (locally quasi-convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc-component of the group is exactly the union of the one-parameter subgroups. We also prove that for metrizable separable locally arc-connected reflexive groups, the exponential map from the Lie algebra into the group is open.
Autores: Aussenhofer, L.; Chasco, María Jesús; Domínguez, X. ;
Revista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN 0022-247X  Vol. 425  Nº 1  2015  págs. 337 - 348
In this article we study the arcwise connected component in the Pontryagin dual of an abelian topological group. It is clear that the set of continuous characters that can be lifted over the reals is contained in the arcwise connected component of the dual group. We show that the converse is true if all arcs in the character group are equicontinuous sets. This property is present in Pontryagin duals of pseudocompact groups, of reflexive groups and of groups which are k-spaces as topological spaces. We study the meaning of such a property and its presence in groups and vector spaces endowed with weak topologies. We also characterize the image of the exponential mapping of a dual group as formed by those characters which can be lifted over the reals endowed with the Bohr topology.
Autores: Bello, H. J.; Chasco, María Jesús; Domínguez, X.;
Revista: ABSTRACT AND APPLIED ANALYSIS
ISSN 1085-3375  2013  págs. 590159
A twisted sum in the category of topological Abelian groups is a short exact sequence 0 -> Y -> X -> Z -> 0 where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to 0 -> Y -> Y x Z -> Z -> 0. We study the class S-TG(T) of topological groups G for which every twisted sum 0 -> T -> X -> G -> 0 splits. We prove that this class contains Hausdorff locally precompact groups, sequential direct limits of locally compact groups, and topological groups with L-infinity topologies. We also prove that it is closed by taking open and dense subgroups, quotients by dually embedded subgroups, and coproducts. As means to find further subclasses of S-TG(T), we use the connection between extensions of the form 0 -> T -> X -> G -> 0 and quasi-characters on G, as well as three-space problems for topological groups. The subject is inspired on some concepts known in the framework of topological vector spaces such as the notion of K-space, which were interpreted for topological groups by Cabello.
Autores: Ardanza-Trevijano, Sergio; Chasco, María Jesús; Domínguez, X.; et al.
Revista: Forum Mathematicum
ISSN 0933-7741  Vol. 24  Nº 2  2012  págs. 289 - 302
Autores: Chasco, María Jesús; Dikranjan, D; Martin-Peinador, E.;
Revista: TOPOLOGY AND ITS APPLICATIONS
ISSN 0166-8641  Vol. 159  Nº 9  2012  págs. 2290-2309
The Pontryagin duality theorem for locally compact abelian groups (briefly. LCA groups) has been the starting point for many different routes of research in Mathematics. From its appearance there was a big interest to extend it in a context broader than LCA groups. Kaplan in the 40's proposed and it still remains open the problem of characterization of all abelian topological groups for which the canonical mapping into its bidual is a topological isomorphism, assuming that the dual and the bidual carry the compact-open topology. Such groups are called reflexive. In this survey we deal with results on reflexivity of certain classes of groups, with special emphasis on the smaller class which better reflects the properties of LCA groups, namely that of strongly reflexive groups. A topological abelian group is said to be strongly reflexive if all its closed subgroups and its Hausdorff quotients as well as the closed subgroups and the Hausdorff quotients of its dual group are reflexive. (C) 2012 Elsevier B.V. All rights reserved.
Autores: Chasco, María Jesús; Domínguez, X.; Tarieladze, V.;
Revista: Topology and its Applications
ISSN 0166-8641  Vol. 158  Nº 3  2011  págs. 484 - 491
Autores: Aubenhofer, Lydia; Chasco, María Jesús; Dikranjan, Dikran; et al.
Revista: Journal of Mathematical Analysis and Applications
ISSN 0022-247X  Vol. 380  Nº 2  2011  págs. 552 - 570
Autores: Chasco, María Jesús; Domínguez, X.; Trigos, J.;
Revista: Topology and its Applications
ISSN 0166-8641  Vol. 158  Nº 14  2011  págs. 1836 - 1843
Autores: Aubenhofer, Lydia; Chasco, María Jesús; Dikranjan, Dikran; et al.
Revista: Journal of Mathematical Analysis and Applications
ISSN 0022-247X  Vol. 370  Nº 2  2010  págs. 431 - 452

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