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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]