Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ...Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.展开更多
基金Project supported by the National Natural Science Foundation ofChina (No. 10171090) and the Scientific Research Fund of ZhejiangProvincial Education Department (No. 20030341) China
文摘Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.
