find a smallest nuclear $C^*$ algebra containing set S [closed]

Suppose $$S$$ is a set ,can we find a smallest nuclear $$C^*$$ algebra containing $$S$$

closed as off-topic by Jendrik Stelzner, YuiTo Cheng, Lee David Chung Lin, steven gregory, CesareoMay 13 at 7:24

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No. There are C$$^*$$-algebras that are not contained in any nuclear C$$^*$$-algebra. Any non-exact algebra would give the counterexample, as exactness passes to subalgebras.
• That would be $A$. – Martin Argerami May 19 at 19:57