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In mathematics, the Suslin operation A is an operation that constructs a set from a collection of sets indexed by finite sequences of positive integers. The Suslin operation was introduced by and . In Russia it is sometimes called the A-operation after Alexandrov. It is sometimes denoted by the symbol (a calligraphic capital letter A). ==Definitions== Suppose we have Suslin scheme, in other words a function ''M'' from finite sequences of positive integers ''n''1,...,''n''''k'' to sets ''M''''n''1,...,''n''''k''. The result of the Suslin operation is the set :''A''(''M'') = ∪ (''M''''n''1 ∩ ''M''''n''1,''n''2 ∩ ''M''''n''1,''n''2, ''n''3 ∩ ...) where the union is taken over all infinite sequences ''n''1,...,''n''''k'',... If M is a family of subsets of a set ''X'', then ''A''(M) is the family of subsets of ''X'' obtained by applying the Suslin operation ''A'' to all collections as above where all the sets ''M''''n''1,...,''n''''k'' are in M. The Suslin operation on collections of subsets of ''X'' has the property that ''A''(''A''(M)) = ''A''(M). The family ''A''(''M'') is closed under taking countable unions or intersections, but is not in general closed under taking complements. If M is the family of closed subsets of a topological space, then the elements of ''A''(M) are called Suslin sets, or analytic sets if the space is a Polish space. 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 operation」の詳細全文を読む スポンサード リンク
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