The Bohr compactification, modulo a metrizable subgroup

W. W. Comfort, F. Javier Trigos-Arrieta, Ta-Sun Wu

Type: Article

Publication Date: 1993-01-01

Citations: 30

DOI: https://doi.org/10.4064/fm-143-2-119-136

Abstract

The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩

Locations

Fundamenta Mathematicae - View - PDF

Similar Works

Action	Title	Year	Authors
+	The Bohr compactification, modulo a metrizable subgroup	1993	W. W. Comfort F. Javier Trigos-Arrieta Ta-Sun Wu
+	A theorem on the Bohr compactification of a locally compact Abelian group	1965	N. Th. Varopoulos
+	The Bohr compactification of an abelian group as a quotient of its Stone–Čech compactification	2020	Pavol Zlatoš
+	The Bohr compactification of an abelian group as a quotient of its Stone-Čech compactification	2018	Pavol Zlatoš
+	The Bohr compactification of an arithmetic group	2025	Bachir Bekka
+	The Bohr compactification of an abelian group as a quotient of its Stone-\v{C}ech compactification	2018	Pavol Zlatoš
+	Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)	1997	W. W. Comfort F. Javier Trigos-Arrieta Ta-Sun Wu
+ PDF Chat	A Theorem of C. Ryll-Nardzewski and Metrizable L.C.A. Groups	1980	L. Thomas Ramsey
+	Remarks on a Theorem of Glicksberg	2020	W. W. Comfort F. Javier Trigos-Arrieta
+	Some remarks on subgroups defined by the Bohr compactification	1983	Robert P. Hunter
+ PDF Chat	A theorem of C. Ryll-Nardzewski and metrizable l.c.a. groups	1980	L. Thomas Ramsey
+	The torsion Bohr topology for Abelian groups	2013	Omar Becerra-Muratalla
+	When a totally bounded group topology is the Bohr topology of a LCA group	2019	Salvador Hernández F. Javier Trigos-Arrieta
+	Abundance of $\sigma$-compact non-compactly generated groups witnessed by the Bohr topology of an abelian group (General and geometric topology today and their problems)	2008	Dikran Dikranjan Dmitri Shakhmatov
+ PDF Chat	Compactness in Hom(<i>G</i>, <i>H</i>)	1970	H. H. Corson Irving Glicksberg
+	The Čech–Stone compactification of a discrete groupoid	1991	Eric K. van Douwen
+	The Bohr compactification of an arithmetic group	2023	Bachir Bekka
+ PDF Chat	Bohr compactifications of a locally compact abelian group I	1943	Hirotada Anzai Shizuo Kakutkni
+	Remarks on the Bohr-torsion topology of a locally compact Abelian group	2017	F. Javier Trigos-Arrieta
+ PDF Chat	On the G-compactifications of the rational numbers	2008	Jan van Mill

Works That Cite This (29)

Action	Title	Year	Authors
+ PDF Chat	On convergent sequences in dual groups	2020	María V. Ferrer Salvador Hernández Mikhail Tkachenko
+	Maximally Almost Periodic Groups and a Theorem of Glicksberg<sup>a</sup>	1996	Ta Sun Wu LEMUEL RIGGINS
+ PDF Chat	The Dual Group of a Dense Subgroup	2004	W. W. Comfort S. U. Raczkowski F. Javier Trigos-Arrieta
+	Totally bounded topological group topologies on the integers	2002	S. U. Raczkowski
+ PDF Chat	On the existence of topologies compatible with a group duality with predetermined properties	2021	Tayomara Borsich Xabier Domínguez Elena Martín-Peinador
+ PDF Chat	Limits in function spaces and compact groups	2004	Joan E. Hart Kenneth Kunen
+	On characterized subgroups of compact abelian groups	2013	Dikran Dikranjan Saak Gabriyelyan
+	A dichotomy property for locally compact groups	2018	María V. Ferrer Salvador Hernández Luis Tárrega
+	Characterizing subgroups of compact abelian groups	2006	Dikran Dikranjan Kenneth Kunen
+	A characterization of Pontryagin–van Kampen duality for locally convex spaces	2002	Fernando Garibay Bonales F. Javier Trigos-Arrieta Rigoberto Vera Mendoza

Works Cited by This (7)

Action	Title	Year	Authors
+ PDF Chat	Topologies induced by groups of characters	1964	W. W. Comfort Keith W. Ross
+	On Almost Periodic Compactifications of Locally Compact Groups	1971	William Moran
+ PDF Chat	Compactness in locally compact groups	1973	Ralph Hughes
+	On sequential convergence in groups	1967	G. A. Reid
+	On the foundations of k̲-group theory	1977	W. F. Lamartin
+	Topological Groups and Semigroups	1988	Yurii I. Lyubich
+	Pseudocompactness on groups	1991	F. Javier Trigos-Arrieta