Pure Mathematics
Mathematical Sciences
Denote by Tthe torus,i.e., the topological group consisting of the complex numbers of modulus 1 under multiplication. Every topological Abelian group (G, t) has associated a weaker topological group topology, denoted by t+, defined as the weakest topology on G that makes the t-continuous homomorphisms (t-characters) ϕ:G→T continuous. The topology t+ is called the Bohr topology on (G, t). Let T denote the torsion subgroup of T. Then the weakest topology that makes the t-characters ϕ:G→T continuous is called the Bohr-torsion topology on (G, t) and is denoted by t⊕. When t is locally compact, we show that t⊕ is Hausdorff if and only if (G, t) is zero dimensional, and if (G, t) is zero dimensional and H is a subgroup of G, then H is t-closed if and only if H is t⊕-closed.
en
articles
http://link.springer.com/10.1007%2Fs40590-017-0161-y
https://scigraph.springernature.com/explorer/license/
2018-10-01
false
Remarks on the Bohr-torsion topology of a locally compact Abelian group
2019-04-11T02:11
2018-10
research_article
373-380
2296-4495
0037-8615
Boletín de la Sociedad Matemática Mexicana
10.1007/s40590-017-0161-y
doi
24
2
Department of Mathematics, California State University, Bakersfield, 93311, Bakersfield, CA, USA
California State University, Bakersfield
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readcube_id
pub.1083894346
dimensions_id
F. Javier
Trigos-Arrieta
Springer Nature - SN SciGraph project