F. Javier Trigos-Arrieta
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
F. Javier Trigos-Arrieta has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Salvador Hernández
Universitat Jaume I, Departamento de Matemáticas, Campus de Riu Sec, 12071 Castellón, Spain
7 shared publications - I. Sepúlveda
Universitat Jaume I, Departamento de Matemáticas, Campus de Riu Sec, 12071 Castellón, Spain
3 shared publications - Maria Vincenta Ferrer
Universitat Jaume I, Departamento de Matemáticas, Campus de Riu Sec, 12071 Castellón, Spain
3 shared publications - Dieter Remus
Institut für Mathematik , Universität Paderborn , Warburger Str. 100, 33098 Paderborn , Germany
2 shared publications - Maria Jesus Chasco
Universidad de Navarra
1 shared publication - S. U. Raczkowski1 shared publication
Latest Publications
- Open Access
- 4 December 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (53) , 612-623
The Baire property and precompact duality
We prove that if G G is a totally bounded Abelian group such that its dual group G ^ p \widehat {G}_p equipped with the finite-open topology is a Baire group, then every compact subset of G G must be finite. This solves an open question by Chasco, Domínguez, and Tkachenko. Among other consequences, we obtain an example of a group that is g g -dense in its completion but is not g g -barreled. This solves a question proposed by Außenhofer and Dikranjan.
- 4 December 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (53) , 612-623
Open AccessThe Baire property and precompact duality
We prove that if G G is a totally bounded Abelian group such that its dual group G ^ p \widehat {G}_p equipped with the finite-open topology is a Baire group, then every compact subset of G G must be finite. This solves an open question by Chasco, Domínguez, and Tkachenko. Among other consequences, we obtain an example of a group that is g g -dense in its completion but is not g g -barreled. This solves a question proposed by Außenhofer and Dikranjan.
- Open Access
The Baire property and precompact duality
We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au$β$enhofer and Dikranjan.}Open AccessThe Baire property and precompact duality
We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au$β$enhofer and Dikranjan.} - Open Access
- 1 January 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (53) , 612-623
The Baire property and precompact duality
We prove that if $G$ is a totally bounded Abelian group such that its dual group $\widehat {G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez, and Tkachenko. Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barreled. This solves a question proposed by Außenhofer and Dikranjan.- 1 January 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society, Series B
- Vol. 11 (53) , 612-623
Open AccessThe Baire property and precompact duality
We prove that if $G$ is a totally bounded Abelian group such that its dual group $\widehat {G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez, and Tkachenko. Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barreled. This solves a question proposed by Außenhofer and Dikranjan. - 28 September 2022
- Published by Walter de Gruyter GmbH in Journal of Group Theory
On closed subgroups of precompact groups
It is a theorem of W. W. Comfort and K. A. Ross that if 𝐺 is a subgroup of a compact Abelian group and 𝑆 denotes the continuous homomorphisms from 𝐺 to the one-dimensional torus, then the topology on 𝐺 is the initial topology given by 𝑆. Assume that 𝐻 is a subgroup of 𝐺. We study how the choice of 𝑆 affects the topological placement and properties of 𝐻 in 𝐺. Among other results, we have made significant progress toward the solution of the following specific questions. How many totally bounded group topologies does 𝐺 admit such that 𝐻 is a closed (dense) subgroup? If denotes the poset of all subgroups of 𝐺 that are 𝑆-closed, ordered by inclusion, does have a greatest (resp. smallest) element? We say that a totally bounded (topological, resp.) group is an SC group (topologically simple, resp.) if all its subgroups are closed (if 𝐺 and are its only possible closed normal subgroups, resp.) In addition, we investigate the following questions. How many SC-(topologically simple totally bounded, resp.) group topologies does an arbitrary Abelian group 𝐺 admit?- 28 September 2022
- Published by Walter de Gruyter GmbH in Journal of Group Theory
On closed subgroups of precompact groups
It is a theorem of W. W. Comfort and K. A. Ross that if 𝐺 is a subgroup of a compact Abelian group and 𝑆 denotes the continuous homomorphisms from 𝐺 to the one-dimensional torus, then the topology on 𝐺 is the initial topology given by 𝑆. Assume that 𝐻 is a subgroup of 𝐺. We study how the choice of 𝑆 affects the topological placement and properties of 𝐻 in 𝐺. Among other results, we have made significant progress toward the solution of the following specific questions. How many totally bounded group topologies does 𝐺 admit such that 𝐻 is a closed (dense) subgroup? If denotes the poset of all subgroups of 𝐺 that are 𝑆-closed, ordered by inclusion, does have a greatest (resp. smallest) element? We say that a totally bounded (topological, resp.) group is an SC group (topologically simple, resp.) if all its subgroups are closed (if 𝐺 and are its only possible closed normal subgroups, resp.) In addition, we investigate the following questions. How many SC-(topologically simple totally bounded, resp.) group topologies does an arbitrary Abelian group 𝐺 admit?- Open Access
On closed subgroups of precompact groups
It is a Theorem of W.~ W. Comfort and K.~ A. Ross that if $G$ is a subgroup of a compact Abelian group, and $S$ denotes those continuous homomorphisms from $G$ to the one-dimensional torus, then the topology on $G$ is the initial topology given by $S$. {Assume that $H$ is a subgroup of $G$. We study how} the choice of $S$ affects the topological placement and properties of $H$ in $G$. Among other results, we have {made significant} progress toward the solution of the following specific questions: How many totally bounded group topologies does $G$ admit such that $H$ is a closed (dense) subgroup? If $C_S$ denotes the poset of all subgroups of $G$ that are $S$-closed, ordered by inclusion, does $C_S$ has a greatest (resp. smallest) element? We say that a totally bounded (topological, resp.) group is an \textit{SC-group} (\textit{topologically simple}, resp.) if all its subgroups are closed (if $G$ and $\{e\}$ are its only possible closed normal subgroups, resp.) {In addition, we investigate the following questions.} How many SC-(topologically simple totally bounded, resp.) group topologies does an arbitrary Abelian group $G$ admit?Open AccessOn closed subgroups of precompact groups
It is a Theorem of W.~ W. Comfort and K.~ A. Ross that if $G$ is a subgroup of a compact Abelian group, and $S$ denotes those continuous homomorphisms from $G$ to the one-dimensional torus, then the topology on $G$ is the initial topology given by $S$. {Assume that $H$ is a subgroup of $G$. We study how} the choice of $S$ affects the topological placement and properties of $H$ in $G$. Among other results, we have {made significant} progress toward the solution of the following specific questions: How many totally bounded group topologies does $G$ admit such that $H$ is a closed (dense) subgroup? If $C_S$ denotes the poset of all subgroups of $G$ that are $S$-closed, ordered by inclusion, does $C_S$ has a greatest (resp. smallest) element? We say that a totally bounded (topological, resp.) group is an \textit{SC-group} (\textit{topologically simple}, resp.) if all its subgroups are closed (if $G$ and $\{e\}$ are its only possible closed normal subgroups, resp.) {In addition, we investigate the following questions.} How many SC-(topologically simple totally bounded, resp.) group topologies does an arbitrary Abelian group $G$ admit? - 1 June 2019
- Published by Elsevier in Topology and its Applications
- Vol. 259, 110-123
When a totally bounded group topology is the Bohr topology of a LCA group
- 1 June 2019
- Published by Elsevier in Topology and its Applications
- Vol. 259, 110-123
When a totally bounded group topology is the Bohr topology of a LCA group
- Open Access
When a totally bounded group topology is the Bohr Topology of a LCA group
We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a totally bounded abelian group $(G,w)$ is the Bohr reflection of a locally compact abelian group. Necessary and sufficient conditions are established in terms of the inner properties of $w$. As an application, an example of a MAP group $(G,t)$ is given such that every closed, metrizable subgroup $N$ of $bG$ with $N \cap G = \{0\}$ preserves compactness but $(G,t)$ does not strongly respects compactness. Thereby, we respond to Questions 4.1 and 4.3 in [comftrigwu].Open AccessWhen a totally bounded group topology is the Bohr Topology of a LCA group
We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a totally bounded abelian group $(G,w)$ is the Bohr reflection of a locally compact abelian group. Necessary and sufficient conditions are established in terms of the inner properties of $w$. As an application, an example of a MAP group $(G,t)$ is given such that every closed, metrizable subgroup $N$ of $bG$ with $N \cap G = \{0\}$ preserves compactness but $(G,t)$ does not strongly respects compactness. Thereby, we respond to Questions 4.1 and 4.3 in [comftrigwu]. - 17 February 2017
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 24 (2) , 373-380
Remarks on the Bohr-torsion topology of a locally compact Abelian group
- 17 February 2017
- Published by Springer Nature in Boletín de la Sociedad Matemática Mexicana
- Vol. 24 (2) , 373-380
Remarks on the Bohr-torsion topology of a locally compact Abelian group
- Open Access
Products of finite groups and nonmeasurable subgroups
It is proven that if $G$ is a finite group, then $G^\omega$ has $2^{\mathfrak c}$ dense nonmeasurable subgroups. Also, other examples of compact groups with dense nonmeasurable subgroups are presented.Open AccessProducts of finite groups and nonmeasurable subgroups
It is proven that if $G$ is a finite group, then $G^\omega$ has $2^{\mathfrak c}$ dense nonmeasurable subgroups. Also, other examples of compact groups with dense nonmeasurable subgroups are presented. - 2 July 2011
- Published by Elsevier in Topology and its Applications
- Vol. 158 (14) , 1836-1843
Some cases of preservation of the Pontryagin dual by taking dense subgroups
- 2 July 2011
- Published by Elsevier in Topology and its Applications
- Vol. 158 (14) , 1836-1843
Some cases of preservation of the Pontryagin dual by taking dense subgroups