Geodesic
A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings
Filomat, Tome 34 (2020) no. 9, p. 2897

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Suppose G is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on G which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for completeness of different types of bounded group homomorphisms between topological rings have been obtained, as well.
DOI : 10.2298/FIL2009897Z
Classification : 54H12, 13J99, 20K30, 47B65
Keywords: Locally solid ℓ-group, bounded homomorphism, unbounded topology, Fatou property, topological ring, completeness 
Omid Zabeti. A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings. Filomat, Tome 34 (2020) no. 9, p. 2897 . doi: 10.2298/FIL2009897Z
@article{10_2298_FIL2009897Z,
     author = {Omid Zabeti},
     title = {A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings},
     journal = {Filomat},
     pages = {2897 },
     year = {2020},
     volume = {34},
     number = {9},
     doi = {10.2298/FIL2009897Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2009897Z/}
}
TY  - JOUR
AU  - Omid Zabeti
TI  - A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings
JO  - Filomat
PY  - 2020
SP  - 2897 
VL  - 34
IS  - 9
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2009897Z/
DO  - 10.2298/FIL2009897Z
LA  - en
ID  - 10_2298_FIL2009897Z
ER  - 
%0 Journal Article
%A Omid Zabeti
%T A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings
%J Filomat
%D 2020
%P 2897 
%V 34
%N 9
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2009897Z/
%R 10.2298/FIL2009897Z
%G en
%F 10_2298_FIL2009897Z

Cité par Sources :