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Cocountability : ウィキペディア英語版 | Cocountability In mathematics, a cocountable subset of a set ''X'' is a subset ''Y'' whose complement in ''X'' is a countable set. In other words, ''Y'' contains all but countably many elements of ''X''. While the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says ''Y'' is cofinite. == σ-algebras ==
The set of all subsets of ''X'' that are either countable or cocountable forms a σ-algebra, i.e., it is closed under the operations of countable unions, countable intersections, and complementation. This σ-algebra is the countable-cocountable algebra on ''X''. It is the smallest σ-algebra containing every singleton set.
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「Cocountability」の詳細全文を読む
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