| Applied Mathematics |
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| A general version of the Morse-Sard theorem |
| JIANG Hai-yi |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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Abstract Let k, m, n be positive integers, and k≤2, α∈(0,1], 0k,α(Rm, 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.
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Received: 30 September 2003
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