“无限可微函数的几个定理的新证明[1]”一文的错误(英文)

Mistakes in the paper“New proofs of Some theorems on infinitely differentiable functions”[Ⅰ]

中文摘要:

      

英文摘要:

      In the paper [1], the author told us that he provides new proofs for the three classical theorems on real singularity theory: Mather's two theorms, and the splitting lemma. And in the paper [2], the author used this method to catastrophe theory.The journal "Mathematical Reviews" ever commented the above papers successively in Vol.57, No.3 (1979) and Vol.58, No.3 (1979).This paper points out that the proofs about Mather′s theorems Ⅰand Ⅱ in [1] are wrong, and then presents an counter-example to show that the corollary and conjecture are false.