Field of sets

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 $X$ .

单词	Stone field
释义	Stone field 英语百科 Field of sets 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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Stone field

Field of sets