Re: Stone duality for generalized Boolean algebras

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

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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