A CHARACTERISTIC PROPERTY OF THE SPACE s.

It is shown that under certain stability conditions a complemented subspace of the space s of rapidly decreasing sequences is isomorphic to s and this condition characterizes s. This result is used to show that, for the classical Cantor set X, the space C∞(X) of restrictions to X of C∞-functions on R is isomorphic to s, which leads to an improvement of the theory developed in a previous work of the author. [ABSTRACT FROM AUTHOR]