Raikov completion and the Hartman-Mycielski construction

• Autores: María Montserrat Bruguera Padró
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 157-165
• Idioma: inglés
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• Resumen

  • Hartman and Mycielski proved that every topological group G is topologically isomorphic to a closed subgroup of a connected, locally connected topological group. Analyzing the Hartman--Mycielski construction, one can verify that the group and its Hartman--Mycielski completion share many properties such as metrizability, separability, and omega-narrowness. Further, if G is Abelian, divisible, torsion, or torsion-free, so is its Hartman--Mycielski completion.

    It is easy to see that the Hartman--Mycielski completion of a group is not Raikov complete, except for the trivial case |G| = 1. However, for a metrizable group G, we describe the Raikov completion of a group in terms of known objects of Topological Algebra and Functional Analysis.