We extend work of the first author concering relative double commutants and
approximate double commutants of unital subalgebras of unital C*-algebras,
including metric versions involving distance estimates. We prove metric results
for AH subalgebras of von Neumann algebras or AF subalgebras of primitive
C*-algebras. We prove other general results, including some for nonselfadjoint
commutative subalgebras, using C*-algebraic versions of the Stone-Weierstrass
and Bishop-Stone-Weierstrass theorems.