Article contents
Local Homomorphisms of Topological Groups
Published online by Cambridge University Press: 09 April 2009
Abstract
A mapping f : G → s from a left topological group G into a semigroup S is a local homomorphism if for every x є G \ {e}, there is a neighborhood Ux of e such that f (xy) = f (x)f (y) for all y є Ux \ {e}. A local homomorphism f : G → S is onto if for every neighborhood U of e, f(U \ {e}) = S. We show that
(1) every countable regular left topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto N,
(2) 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,
(3) it is consistent that every countable nondiscrete maximally almost periodic topological group admits a local homomorphism onto the countably infinite right zero semigroup.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 2007
References
- 4
- Cited by