Regular open sets
The purpose of this section is to discuss one more example of a Boolean algebra. This example, the most intricate of all the ones so far, is one in which the elements of the Boolean algebra are subsets of a set, but the operations are not the usual set-theoretic ones, so that the Boolean algebra is not a field of sets. Artificial examples of this kind are not hard to manufacture; the example that follows arises rather naturally and plays an important role in the general theory of Boolean algebras.
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