For a mapping ϕ : S → T, let ker ϕ = {(u, v) : ϕ(u) = ϕ(v)}
be the kernel of ϕ.
Theorem 5.5
An A-generated profinite semigroup S is a continuous
homomorphic image of ΩAV if and only if it is a pro-V semigroup.
Corollary 5.6
Let S be a pro-V semigroup and suppose that ϕ : S → T is a
continuous homomorphism onto a finite semigroup. Then
T ∈ V.
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