Let Γ be a class of subsets of Baire space (ωω) closed under inverse images by continuous functions. We say such a Γ is continuously closed. Let , the class dual to Γ, consist of the complements relative to ωω of members of Γ. If Γ is not selfdual, i.e., , then let . A continuously closed nonselfdual class Γ of subsets of ωΓ is said to have the first separation property  if
The set C is said to separate A and B. The class Γ is said to have the second separation property  if
We shall assume the axiom of determinateness and show that if Γ is a continuously closed class of subsets of ωω and then
(1) Γ has the first separation property iff does not have the second separation property, and
(2) either Γ or has the second separation property.
Of course, (1) and (2) taken together imply that Γ and cannot both have the first separation property.
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