Stone's representation theorem for Boolean algebras: Difference between revisions

Revision as of 03:13, 1 November 2004

Revision as of 10:41, 24 November 2004

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In detail, the Stone space of a Boolean algebra ''A'' is the set of all 2-valued homomorphisms on ''A'', with the topology of [[pointwise convergence]] of [[net (mathematics)|nets]] of such homomorphisms.

(An alternative and equivalent way to construct the Stone space of ''A'' is as the set of all [[Boolean algebra|maximal idealsultrafilter]]s in ''A'', with the sets {''MU'' : ''MU'' is aan maximal ideal that doesn'tultrafilter containcontaining ''a''} for ''a'' in ''A'' as [[base (topology)|base]] of the topology. In the sequel we will use the homomorphism approach.)

Every Boolean algebra is isomorphic to the algebra of [[clopen]] (i.e., simultaneously closed and open) subsets of its Stone space. The isomorphism maps any element ''a'' of ''A'' to the set of homomorphisms that map ''a'' to 1.

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* [[list of Boolean algebra topics]]

* [[Field of sets]]

* [[Stone duality]]

[[Category:General topology]]