In the paper [2] the following theorem isshowu: Theorem (Th. 3,5, [2]), Ira = 0 or 6 = oo or a> 6, then a closure space X is an absolute extensor for the category of -closure spaces iff a contraction of X is the closure space of all -filters in an -semidistribntive lattice.
In the case when a = ~o and 6 = oo, this theorem becomes Scott's theorem:
Theorem ([7]). A topologieM space X is an absolute extensor for the category of all topological spaces iff a contraction of X is a topological space of "Scott's open sets" in a continuous lattice.
On the other hand, when a = 0 and 6 = o), this theorem becomes Jankowski's theorem :
Theorem ([4]). A closure space X is an absolute extensor for the category of all closure spaces satisfying the compactness theorem iff a contraction of X is a closure space of all filters in a complete Keyting lattice.
But for separate cases of a and 6, the Theorem 3.5 from [2] is proved using essen. tialy different methods.
In this paper it is shown that this theorem can be proved using, for retraction, one uniform formula.
hramely it is proved that if a = 0 or 6 = ~ or a > 6 and F~,~ (L) c B ~ and if 15 is an -semidistributive lattice, then the function r: B~,~ ~2'~,~ (/~) such that for x e ~(u): (\*) r(x) = i~fL{1 e ~1 (VA ~\_ ~) x e C(A) ~l e C(A)} defines retraction, where C is a proper closure operator for B ~ CGt~ 9