- Tytuł:
- The concept of boundedness and the Bohr compactification of a MAP Abelian group
- Autorzy:
-
Galindo, Jorge
Hernández, Salvador - Powiązania:
- https://bibliotekanauki.pl/articles/1205259.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Bohr topology
LCA group
$ℒ_∞$-group
boundedness
locally convex vector space
DF-space
maximally almost periodic
respects compactness
C-embedded
C*-embedded - Opis:
- Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an $ℒ_∞$-group, contains "many" discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This result generalizes an analogous theorem of van Douwen for the discrete case and some other ones due to Hartman and Ryll-Nardzewski concerning the existence of $I_0$-sets. We also obtain some results on preservation of compactness for the Bohr topology of several types of MAP Abelian groups, like $ℒ_∞$-groups, locally convex vector spaces and free Abelian topological groups.
- Źródło:
-
Fundamenta Mathematicae; 1999, 159, 3; 195-218
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł