中文摘要：

设M和N是C^r（r≥1）Banach流形，P包含N是N的子流形，f是从M到N的C^1映射．该文引进映射f在x0∈f^-1（P）点与P广义横截的概念，它是经典的横截概念的推广．接着讨论了广义横截性和广义正则点的关系，证明：映射f在x0点与P广义横截的充分必要条件为x0是与f相关的某个映射g的广义正则点；当子流形P退化成单点集时，若映射f与P={p}广义横截，作者证明p是f的广义正则值；最后证明了广义横截点的全体O={x∈f^-1（P）：fψ↓^x G P}是开集．

英文摘要：

In this paper, the authors generalize the classical transversality by using the perturbation theory of generalized inverse of linear bounded operator, get the new concept of generalized transversality. The authors also discuss some basic properties of the generalized transversality and the relations between generalized transversality and generalized regular point.