Re: Stone duality for generalized Boolean algebras

["Fred E.J. Linton" <fejlinton@usa.net>]

The Boolean rng counterpart to the Stone duality, identifying
Boolean algebras with the opposite of compact T2 0-dim'l spaces,
exploits the fact that the category of boolean rngs amounts to
the category of *augmented* Boolean algebras (the slice category
BA | 2 of 2-valued boolean homomorphisms from Boolean algebras) --
true because *kernel* gives an equivalence from latter to former --
hence is equivalent to the opposite of *pointed* compact T2 0-dim'l
spaces (and base-point-preserving continuous functions).

While the complement of the base point (in such a pointed space)
may be locally compact, that observation is far from functorial, 
so there's not much good any category of locally compact T2 0-dim'l
spaces will do you.

HTH. Cheers, -- Fred



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