  Based on the Ambegaokar-Eckern-Schon approach to the Coulomb blockade we
develop a complete quantum theory of the single electron transistor. We
identify a previously unrecognized physical observable q^\prime in the problem
that, unlike the usual average charge (Q) on the island, is robustly quantized
for any finite value of the tunneling conductance as the temperature goes to
absolute zero. This novel quantity is fundamentally related to the
non-symmetrized noise of the system. We present a unifying scaling diagram in
the q^\prime - g^\prime plane where g^\prime denotes the conductance of the
system. The results display all the super universal topological features of the
theta-angle concept that previously arose in the theory of the quantum Hall
effect.
