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In mathematics, a Suslin representation of a set of reals (more precisely, elements of Baire space) is a tree whose projection is that set of reals. More generally, a subset ''A'' of κω is λ-Suslin if there is a tree ''T'' on κ × λ such that ''A'' = p(). By a tree on κ × λ we mean here a subset ''T'' of the union of κ''i'' × λ''i'' for all ''i'' ∈ N (or ''i'' < ω in set-theoretical notation). Here, p() = is the ''projection of ''T'', where () = is the set of branches through ''T''. Since () is a closed set for the product topology on κω × λω where κ and λ are equipped with the discrete topology (and all closed sets in κω × λω come in this way from some tree on κ × λ), λ-Suslin subsets of κω are projections of closed subsets in κω × λω. When one talks of ''Suslin sets'' without specifying the space, then one usually means Suslin subsets of R, which descriptive set theorists usually take to be the set ωω. ==See also== *Suslin cardinal *Suslin operation 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Suslin representation」の詳細全文を読む スポンサード リンク
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