ABSTRACT

By properties of K, K-l (K (x)) = H-l (H(x)) for any x V, and there exists a smooth extension of K(x) = (H(x)) l / n inside V.

Given a function F and a set [A] , we denote the restriction of F to [A] as FA. In particular, if F C( ;R), then F o C( , R) and

• FV o (x) = FV(x) for x V; • FU o (x) = (FU o K-1)o K for x U; • FK := FU o K-1 maps [0, K*] into R; • F o (X) = FV(x)1V(x) + FK(K(x))1 \V(x) for x .