The maximal omega-narrow group topology on Abelian groups

• Autores: Lorenzo de Leo, Mikhail G. Tkachenko
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 215-227
• Idioma: inglés
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• Resumen

  • For an Abelian group G, we consider the maximal omega-narrow group topology T on G induced by all homomorphisms of G to second-countable topological Abelian groups. We study the properties of the topological group (G,T) and we prove, among other results, that every uncountable Abelian group equipped with the maximal omega-narrow topology is a first category space which is neither a P-group nor R-factorizable. A comparison of the maximal omega-narrow group topology and the Bohr topology on Abelian groups is also presented.