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  "body": "\n## Summary\n\nA Boolean product is a [[subdirect product|88WN3AD2VQ]] of [[algebras|QJGPT2W0FT]] indexed by the points of a [[Stone space|ZV38HA5PAQ]].\nIts elements behave like continuous functions on that space.\nThe sets where two elements agree are clopen, and elements can be cut and pasted along clopen sets.\nBoolean products give sheaf-like representations of algebras.\nThey are a central tool in the study of discriminator varieties.\n\n## Explanations\n\n### L1 human\n\nThink of an element of a Boolean product as a function on a totally disconnected space, taking its value at each point in a factor algebra.\nTwo such functions agree on a set that is both open and closed.\nGiven two elements and a clopen set, you can take the first element on the clopen set and the second one elsewhere, and the result is again an element.\nEvery Boolean algebra is a Boolean product of copies of the two-element Boolean algebra, over its Stone space.\n",
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