Field of Sets
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See: Set Field, Mathematical Field.
References
- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Field_of_sets
- In mathematics a field of sets is a pair <X, Ƒ> where [math]\displaystyle{ X }[/math] is a set and Ƒ is an algebra over [math]\displaystyle{ X }[/math] i.e., a non-empty subset of the power set of [math]\displaystyle{ X }[/math] closed under the intersection and union of pairs of sets and under complements of individual sets. In other words Ƒ forms a subalgebra of the power set Boolean algebra of X. (Many authors refer to Ƒ itself as a field of sets.) Elements of [math]\displaystyle{ X }[/math] are called points and those of Ƒ are called complexes.