Both compact and sequentially compact sets in Abelian topological group
type: Item
instance of: scholarly article
title: Both compact and sequentially compact sets in Abelian topological group
zbMATH Open document ID: 1230.54030
author: Ronglu Li
author: Hao Guo
author: Charles Swartz
published in: Topology and its Applications
publication date: 2011-07-07T00:00:00Z
review text: The authors consider convergent series in Abelian topological groups. They prove several technical results which make it possible to establish the following fact: if \(G\) is a Hausdorff Abelian topological group and a function \(\mu: 2^\omega\to G\) is countably additive, then its range \(\{\mu(A): A\in 2^\omega\}\) is compact and metrizable. Here \(2^\omega=\{A:A\subset \omega\}\). The developed techniques are also used to obtain some results on relative compactness in locally convex spaces.
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 5918213
zbMATH Keywords: compact
zbMATH Keywords: sequentially compact
zbMATH Keywords: abelian topological group
zbMATH Keywords: convergent series
reviewed by: Vladimir Tkachuk
MaRDI profile type: Publication
full work available at URL: j.topol.2011.05.001
OpenAlex ID: W2025339089
cites work: Q3539552
cites work: Locally convex spaces containing no copy of \(c_ 0\)
cites work: Q4286348
cites work: Operator matrices on topological vector spaces
cites work: The Range of a Vector-Valued Measure
cites work: Q4148368
cites work: Q5605131
cites work: Q4178057
cites work: Q5637596
cites work: Q5603468
cites work: Q5655915
cites work: Theorems of the Orlicz-Pettis-type for locally convex spaces
DOI: 10.1016/J.TOPOL.2011.05.001
description: scientific article; zbMATH DE number 5918213