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Field of sets : ウィキペディア英語版
Field of sets

In mathematics a field of sets is a pair \langle X, \mathcal \rangle where X is a set and \mathcal is an algebra over X i.e., a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of individual sets. In other words \mathcal forms a subalgebra of the power set Boolean algebra of X . (Many authors refer to \mathcal itself as a field of sets. The word "field" in "field of sets" is not used with the meaning of field from field theory.) Elements of X are called points and those of \mathcal are called complexes and are said to be the admissible sets of X .
Fields of sets play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets.
== Fields of sets in the representation theory of Boolean algebras ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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