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词汇 Set algebra
分类 英语词汇 英语翻译词典
释义

Set algebra

中文百科

集合域 Field of sets

(重定向自Set algebra)

在数学中,集合域是有序对<X, F>,其中 X 是集合,F 是 X 上的代数。

  • F 是 X 的幂集布尔代数的子代数。在明确上下文时,亦称 F 为集合域。
  • X 的元素称为,而 F 的元素称为复形

集合域在布尔代数的表示理论中扮演中心角色。所有布尔代数都可以被表示为集合域。

英语百科

Field of sets 集合域

(重定向自Set algebra)

In mathematics a field of sets is a pair \langle X, \mathcal{F} \rangle where X is a set and \mathcal{F} 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{F} forms a subalgebra of the power set Boolean algebra of X . (Many authors refer to \mathcal{F} 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{F} are called complexes and are said to be the admissible sets of X .

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