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- W3211338403 abstract "A closed subgroup of a topological group is a if there is a continuous cross section from to — that is, a continuous function Γ such that ∘ Γ = id (with : → the natural homomorphism).The symbol denotes an Abelian group with its Bohr topology, i.e., the topology induced by .A topological group is (#) [resp., (#)] if is a ccs-subgroup [resp., is a retract] in every group of the form containing as a (necessarily closed) subgroup. One then writes ∈ (#) [resp., ∈ (#)].Theorem 1. Every ccs-subgroup of a group of the form is a retract of (and is homeomorphic to () × ); hence (#) ⊆ (#).Theorem 2. ∈ (#) [resp., ∈ (#)] iff is a ccs-subgroup of its divisible hull (()) [resp., is a retract of (())].Theorem 3. (a) Every cyclic group is in (#).(b) The classes (#) and (#) are closed under finite products.(c) Not every Abelian group is in (#).The following corollary to Theorem 3 answer a question of KUNEN:Corollary. The spaces ((ℤ)) and (((ℤ)/ℤ) × ℤ) are homeomorphic." @default.
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- W3211338403 date "2001-06-01" @default.
- W3211338403 modified "2023-09-23" @default.
- W3211338403 title "Cross Sections and Homeomorphism Classes of Abelian Groups Equipped with the Bohr Topology" @default.
- W3211338403 hasPublicationYear "2001" @default.
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