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Field of sets

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  1. In mathematics a field of sets is a pair \langle X, \mathcalF \rangle where X is a set and \mathcalF 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

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 2, 2008
  2. In other words \mathcalF forms a subalgebra of the power set Boolean algebra of X . (Many authors refer to \mathcalF itself as a field of sets.) Elements of X are called points and those of \mathcalF are called complexes

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 2, 2008
  3. a mathematical structure of sets in an abstract space

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 2, 2008
  4. Fields of sets play an essential role in the representation theory of Boolean algebras

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 2, 2008
  5. Every Boolean algebra can be represented as a field of sets

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 2, 2008
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