  We prove constructive versions of various usual results related to the
Gelfand duality. Namely, that the constructive Gelfand duality extend to a
duality between commutative nonunital C*-algebras and locally compact
completely regular locales, that ideals of a commutative C*-algebras are in
order preserving bijection with the open sublocales of its spectrum, and a
purely constructive result saying that a commutative C*-algebra has a
continuous norm if and only its spectrum is open. We also extend all these
results to the case of localic C*-algebras. In order to do so we develop the
notion of one point compactification of a locally compact regular locale and of
unitarization of a C*-algebra in a constructive framework.
