On $T$-sequences and characterized subgroups

Simple item page
dc.creatorGabriyelyan, S. S.
dc.date2009-02-04
dc.date2009-03-08
dc.date.accessioned2026-07-07T12:49:48Z
dc.date.available2026-07-07T12:49:48Z
dc.descriptionLet $X$ be a compact metrizable abelian group and $\mathbf{u}=\{u_n\}$ be a sequence in its dual $X^{\wedge}$. Set $s_{\mathbf{u}} (X)= \{x: (u_n,x)\to 1\}$ and $\mathbb{T}_0^H = \{(z_n)\in \mathbb{T}^{\infty} : z_n\to 1 \}$. Let $G$ be a subgroup of $X$. We prove that $G=s_{\mathbf{u}} (X)$ for some $\mathbf{u}$ iff it can be represented as some dually closed subgroup $G_{\mathbf{u}}$ of ${\rm Cl}_X G \times \mathbb{T}_0^H$. In particular, $s_{\mathbf{u}} (X)$ is polishable. Let $\mathbf{u}=\{u_n\}$ be a $T$-sequence. Denote by $(\widehat{X}, \mathbf{u})$ the group $X^{\wedge}$ equipped with the finest group topology in which $u_n \to 0$. It is proved that $(\widehat{X}, \mathbf{u})^{\wedge} =G_{\mathbf{u}}$ and $\mathbf{n} (\widehat{X}, \mathbf{u}) = s_{\mathbf{u}} (X)^{\perp}$. We also prove that the group generated by a Kronecker set can not be characterized.
dc.identifierhttps://arxiv.org/abs/0902.0723
dc.identifierhttp://arxiv.org/abs/0902.0723
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222496
dc.subjectGeneral Topology
dc.subjectGroup Theory
dc.subject22-xx
dc.titleOn $T$-sequences and characterized subgroups
dc.typetext

Files

Collections

arXiv