A general version of the Morse-Sard theorem.
Let k, m, n be positive integers, and k> or =2, alphain(0,1], 0<r<min[m,n] an integer, d=r+(m-r)/(k+alpha), and if finC(k,alpha)(Rm, Rn), A=Cr(f)=[xinRm|rank(Df(x))< or =r], then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k> or =2.
Jiang
Hai-Yi
HY
Department of Mathematics, Zhejiang University, Hangzhou 310027, China. hyjiang@math.zju.edu.cn
D000465:Algorithms; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D013598:Systems Theory