Stone space

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In topology, and related areas of mathematics, a Stone space is a non-empty compact totally disconnected Hausdorff space.[1] Such spaces are also called profinite spaces.[2] They are named after Marshall Harvey Stone.

A form of Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the Boolean algebra of clopen sets of a Stone space. This isomorphism forms a category-theoretic duality between the categories of Boolean algebras and Stone spaces.

References[edit]

  1. ^ Hazewinkel, Michiel, ed. (2001), "Stone space", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 
  2. ^ Stone space in nLab