A note on closed ideals in rings of smooth functions (Q1119876)

Let M and N be smooth manifolds and let I be an ideal of \(C^{\infty}(M)\). Let \(I^*\) denote the ideal of \(C^{\infty}(M\times N)\) generated by the elements of I considered as functions independent of the N-variable. The technique of Grothendieck's completed projective tensor product is used to prove the main result that if I is closed and finitely generated, then \(I^*\) is also closed.