Received 21 November 2005; revised 31 May 2006
Communicated by G. Willis
Abstract
A mapping f:G\to S from a left topological group G into a semigroup S is a local homomorphism if for every x\in G\setminus \{e\}, there is a neighborhood U_x of e such that f(xy)=f(x)f(y) for all y\in U_x\setminus \{e\}. A local homomorphism f:G\to S is onto if for every neighborhood U of e, f(U\setminus \{e\})=S. We show that

every countable regular left topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto \mathbb {N};

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.
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2000 Mathematics Subject Classification:
primary 22A30, 54H11; secondary 54A35, 54G05

(Metadata: XML, RSS, BibTeX) 
MathSciNet:
MR2354??? 
Z'blattMATH:
pre05231337 
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