Remarks on the Bohr-torsion topology of a locally compact Abelian group View Full Text


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Article Info

DATE

2018-10

AUTHORS

F. Javier Trigos-Arrieta

ABSTRACT

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. More... »

PAGES

373-380

References to SciGraph publications

  • 1979. Sur les espaces à structure uniforme et sur la topologie générale in ŒUVRES SCIENTIFIQUES COLLECTED PAPERS
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    http://scigraph.springernature.com/pub.10.1007/s40590-017-0161-y

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    http://dx.doi.org/10.1007/s40590-017-0161-y

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