Dear George, I do not think that the answer to Andrej Bauer question is trivial, as a matter of fact it is not trivial at all. Andrej or any other able mathematician does not have to know that GBA is equivalent to BA/2. Furthermore, I feel that Fred Linton bringing into consideration the analogy with C* algebras is pointing to Andrej some relevant mathematical questions. greetings e.d. George Janelidze wrote:
Dear Fred,
Please forgive me, but let us distinguish between serious questions and trivialities:
Andrej Bauer asked:
"...How exactly does this extend to generalized Boolean algebras?..."
And the answer is trivial (without quotation marks): The category GBA of what he called generalized Boolean algebras is dually equivalent to the category 1\STONE of pointed Stone spaces. This follows from Stone duality (since GBA is equivalent to BA/2), but also extends it: just as BA is a non-full subcategory of GBA, STONE can be considered as a non-full subcategory of 1\STONE via the functor that adds base points. And this way the dual equivalence between GBA and 1\STONE indeed extends the Stone duality.
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