Resumen de Local homomorphisms of topological groups
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.
