Continuity, boundedness, connectedness and the Lindelöf property for topological groups

DOI10.1016/0022-4049(91)90018-WzbMath0724.22003MaRDI QIDQ2644777

F. Javier Trigos-Arrieta

Publication date: 1991

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

connected componentszero-dimensionaltopological groupscontinuous homomorphismsLCA groupsLindelöf propertyfunctionally bounded

Mathematics Subject Classification ID

Continuous maps (54C05) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Connected and locally connected spaces (general aspects) (54D05) General properties and structure of LCA groups (22B05)

Related Items (16)

Group topologies making every continuous homomorphic image to a compact group connected ⋮ Topological properties of the group of the null sequences valued in an abelian topological group ⋮ Interpolation sets and the Bohr topology of locally compact groups ⋮ Transmission of continuity to the Bohr topology ⋮ Cross sections and pseudo-homomorphisms of topological abelian groups ⋮ Contributions to the Bohr topology by W.W. Comfort ⋮ Topological groups in which all countable subgroups are closed ⋮ Invariance of compactness for the Bohr topology ⋮ Interpolation sets in spaces of continuous metric-valued functions ⋮ Every Uncountable Abelian Group Admits a Nonnormal Group Topology ⋮ Duality properties of bounded torsion topological abelian groups ⋮ Abelian Groups which Satisfy Pontryagin Duality need not Respect Compactness ⋮ The Dual Group of a Dense Subgroup ⋮ Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems ⋮ The dimension of an LCA group in its Bohr topology ⋮ Weakly pseudocompact subsets of nuclear groups

Cites Work

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• On the Bohr compactification
• Extensions of the Pontrjagin duality. I: Infinite products
• Uniform Boundedness for Groups
• Uniqueness in Structure Theorems for LCA Groups
• On Almost Periodic Compactifications of Locally Compact Groups
• k-Groups and Duality
• Compactness in locally compact groups

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