Abstract.It is known that all subspaces of ω 2 1 have the property that every pair of disjoint closed sets can be separated by disjoint G δ -sets (see [4]). It has been conjectured that all subspaces of ω n 1 also have this property for each n < ω. We exhibit a subspace of { α, β, γ ∈ ω 3 1 : α ≤ β ≤ γ} which does not have this property, thus disproving the conjecture. On the other hand, we prove that all subspaces of { α, β, γ ∈ ω 3 1 : α < β < γ} have this property.

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