Weakly Stable Relations and Inductive Limits of C*-algebras

We show that if mathcal{A} is a class of C*-algebras for which the set of formal relations mathcal{R} is weakly stable, then mathcal{R} is weakly stable for the class mathcal{B} that contains mathcal{A} and all the inductive limits that can be constructed with the C*-algebras in mathcal{A}. A set of formal relations mathcal{R} is said to be weakly stable for a class mathcal{C} of C*-algebras if, in any C*-algebra A \in \mathcal{C}, close to an approximate representation of the set mathcal{R} in A there is an exact representation of mathcal{R} in A.