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High Quality Content by WIKIPEDIA articles! In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Stone (1936), and thus named in his honor. Stone was led to it by his study of the spectral theory of operators on a Hilbert space. ... Read more

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High Quality Content by WIKIPEDIA articles! In the mathematical discipline of general topology, Stone??ech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space ?X. The Stone??ech compactification ?X of a topological space X is the largest compact Hausdorff space "generated" by X, in the sense that any map from X to a compact Hausdorff space factors through ?X. If X is a Tychonoff space then the map from X to its image in ?X is a homeomorphism, so X can be thought of as a subspace of ?X. For general topological spaces X, the map from X to ?X need not be injective. ... Read more

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High Quality Content by WIKIPEDIA articles! In mathematics and in theoretical physics, the Stone?von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. The name is for Marshall Stone and John von Neumann. In quantum mechanics, physical observables are represented mathematically by linear operators on Hilbert spaces. For a single particle moving on the real line R, there are two important observables: position and momentum. ... Read more