周青.映射的横截性定理[J].数学研究及应用,1983,3(1):17~20 |
映射的横截性定理 |
Transversality Theorem of Map |
投稿时间:1981-12-02 |
DOI:10.3770/j.issn:1000-341X.1983.01.002 |
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英文摘要: |
Hirsch conjectured: M、N、A are differential manifolds, g∈C∞(A,N), then the set T = {f∈C∞(M,N)|f∈g} is dense in C∞(M,N)and open if g is proper.In this paper, we prove the transversality theorem of map in the Jet bundle.Theorem 1 Let M, N. A be differential manifolds, g∈C∞(A,Jτ(M、N)), then the set T{f∈C∞(M,N)|fτf∈g } is residual in C∞(M,N) and open if g is proper.Theorem 1 contains Thom's transversal ity theorem as a special case. We can obtain Hirsch's conjecture by using theorem 1. |
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