|
In descriptive set theory, a subset of a Polish space is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student . == Definition == There are several equivalent definitions of analytic set. The following conditions on a subspace ''A'' of a Polish space are equivalent: *''A'' is analytic. *''A'' is empty or a continuous image of the Baire space ωω. *''A'' is a Suslin space, in other words ''A'' is the image of a Polish space under a continuous mapping. *''A'' is the continuous image of a Borel set in a Polish space. *''A'' is a Suslin set, the image of the Suslin operation. *There is a Polish space and a Borel set such that is the projection of ; that is, : *''A'' is the projection of a closed set in the cartesian product of ''X'' times the Baire space. *''A'' is the projection of a ''G''δ set in the cartesian product of ''X'' times the Cantor space. An alternative characterization, in the specific, important, case that is Baire space ωω, is that the analytic sets are precisely the projections of trees on . Similarly, the analytic subsets of Cantor space 2ω are precisely the projections of trees on . 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「analytic set」の詳細全文を読む スポンサード リンク
|