Resumen de The maximal omega-narrow group topology on Abelian groups

Lorenzo de Leo, Mikhail G. Tkachenko

• 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.