Decomposability of completely Suslin-additive families
نویسندگان
چکیده
منابع مشابه
Additive Decomposability of Functions over Abelian Groups
Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables.
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Proof. Suppose z is in the RHS. Then, for some f ∈ Y X , z ∈ Sxfx for all x ∈ X. Hence for each x ∈ X there is y = fx so that z ∈ Sxy, so z is in the LHS. Suppose z is in the LHS. Then for each x ∈ X there is some y ∈ Y so that z ∈ Sxy. Hence for each x ∈ X the set Tx = { y : z ∈ Sxy } is not empty. By AC there is a function f ∈ Y x so that, for all x ∈ X, fx ∈ Tx. Hence, for all x ∈ X, z ∈ Sxf...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1981-0612719-6