大范围分析中Fredholm算子的广义横截性定理

Generalized Transversality Theorem for Fredholm Operator in Global Analysis

该文研究了无穷维Banach流形M,S,N间的Fredholm映射F(u,s):M×S→N的广义横截性定理.如果映射F(u,s)广义横截于单点集{■},而且fs(u)=F(u,s)在外部参数s的意义下是Fredholm映射,那么必然存在一个剩余集∑■S,使得对于任意的s∈∑,fs(u)都广义横截于{■}.

Generalized transversality theorem for Cr mapping F(u,s):M×S→N established in infinite dimensional Banach manifolds M,S,N.If the mapping F(u,s)is generalized transversal to a single point set{■},and fs(u)=F(u,s)is a Fredholm operator in the sense of parameter s,then there exists a residual setΣ■S,such that fs(u)are generalized transversal to{■},for all s∈Σ.