# Homomorphisms on Compact Subsets of βS

Volume 8, Number 2 (2009), 125 - 136

## Homomorphisms on Compact Subsets of βS

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### Abstract

Let S and T be infinite discrete semigroups, let A µ P(S), and assume that A has the finite intersection property. Let f : S !T and let ef : ¯S !¯T be its continuous extension. We obtain necessary and sufficient conditions for the restriction of e T f to A2A c`¯S(A) to be a homomorphism and to be injective. We also investigate certain simpler conditions that are known to be sufficient for this restriction to be a homomorphism.