Dyadic subspaces of subgroups of topological groups
type: Item
instance of: scholarly article
title: Dyadic subspaces of subgroups of topological groups
zbMATH Open document ID: 0617.22006
DOI: 10.1007/BF01060948
author: Yu. V. Tsybenko
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let G be a compact group and let L(G) be the space of all closed subgroups of G with Chabauty topology. It is well known that L(G) is compact. The main result of this paper is the following one. Let G be a compact abelian group. The space L(G) is dyadic (i.e. L(G) is a continuous image of the Cantor cube) iff the weight of G is less then \(\aleph_ 2\). The paper contains also a description of all compact abelian groups G such that the space L(G) contains isolated points. A note. The reviewer has now proved that the Souslin number of the space L(G) is countable for any compact group G. The main result of the paper under review is true for all compact groups.
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 4000241
zbMATH Keywords: dyadic space
zbMATH Keywords: compact group
zbMATH Keywords: closed subgroups
zbMATH Keywords: Chabauty topology
zbMATH Keywords: compact abelian groups
zbMATH Keywords: Souslin number
reviewed by: Igor V. Protasov
MaRDI profile type: Publication
cites work: Limite d'ensembles et géométrie des nombres
cites work: Q3665348
cites work: Dualisms of topological abelian groups
description: scientific article; zbMATH DE number 4000241