Field of Sets

In mathematics a field of sets is a pair where is a set and is an algebra over i.e., a non-empty subset of the power set of closed under the intersection and union of pairs of sets and under complements of individual sets. In other words forms a subalgebra of the power set Boolean algebra of . (Many authors refer to 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 are called points and those of are called complexes.

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.

Famous quotes containing the words field of, field and/or sets:

    The field of doom bears death as its harvest.
    Aeschylus (525–456 B.C.)

    When it had long since outgrown his purely medical implications and become a world movement which penetrated into every field of science and every domain of the intellect: literature, the history of art, religion and prehistory; mythology, folklore, pedagogy, and what not.
    Thomas Mann (1875–1955)

    It is time to be old,
    To take in sail:—
    The god of bounds,
    Who sets to seas a shore,
    Came to me in his fatal rounds,
    And said: ‘No more!’
    Ralph Waldo Emerson (1803–1882)