Local homomorphisms of topological groups

• Autores: Yevhen Zelenyuk
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 1, 2007, págs. 135-148
• Idioma: inglés
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• Resumen

  • A mapping f:GS from a left topological group G into a semigroup S is a local homomorphism if for every xGe , there is a neighborhood Ux of e such that f(xy)=f(x)f(y) for all yUxe . A local homomorphism f:GS is onto if for every neighborhood U of e, f(Ue)=S . We show that every countable regular left topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto ;

    it is consistent that every countable topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto any countable semigroup;

    it is consistent that every countable nondiscrete maximally almost periodic topological group admits a local homomorphism onto the countably infinite right zero semigroup.