منابع مشابه
Characterizing Subgroups of Compact Abelian Groups
We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter.
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The set C(G) of closed subgroups of a locally compact group G has a natural topology which makes it a compact space. This topology has been defined in various contexts by Vietoris, Chabauty, Fell, Thurston, Gromov, Grigorchuk, and many others. The purpose of the talk was to describe the space C(G) first for a few elementary examples, then for G the complex plane, in which case C(G) is a 4–spher...
متن کاملQuasi-convex density and determining subgroups of compact abelian groups
For an abelian topological group G, let Ĝ denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G), and an open neighbourhood U of 0 in T, we show that |{χ ∈ Ĝ : χ(X) ⊆ U}| = |Ĝ|. (Here, w(G) denotes the weight of G.) A subgroup D of G determines G if the map r : Ĝ → D̂ defined ...
متن کاملp–STUBBORN SUBGROUPS OF CLASSICAL COMPACT LIE GROUPS
induces an equivalence of Fp-homology [JMO, §§1-2]. This decomposition of BG, and the category Rp(G), play a central role in [JMO] and [JMO2] as a tool for describing sets of homotopy classes of maps fromBG to BH for any (other) compact connected Lie group H. But in most cases, explicit descriptions of the Rp(G), or explicit lists of the p-stubborn subgroups of G, were not necessary to obtain t...
متن کاملOn T-Characterized Subgroups of Compact Abelian Groups
A sequence {un}n∈ω in abstract additively-written Abelian group G is called a T -sequence if there is a Hausdorff group topology on G relative to which limn un = 0. We say that a subgroupH of an infinite compact Abelian groupX is T -characterized if there is a T -sequence u = {un} in the dual group of X , such that H = {x ∈ X : (un, x) → 1}. We show that a closed subgroupH ofX is T -characteriz...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2016
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgth-2015-0034