关于局部精细点的一个注

A Remark on Locally Fine Point

设 E和 F是 Banach空间 ,让 f是定义在 E中开集 U到 F的一个 C1映射。非线性泛函分析中一个著名的结果是 f的正则点全体是 E中的一个开子集。f 的局部精细点概念是 f 的正则点的推广。由于它的引进解决了许多非线性泛函分析的问题 ,如局部共轭定理和现代分析学中的秩定理等等。因此局部精细点的概念是代替正则点的一个重要的概念。经讨论证明 ,f在 U中的局部精细点全体也是

Let E and F be Banach spaces, and f:UE→F be a C 1 map where U is an open set in E . It is well known that the set of all of regular points of f is an open set in E . Since the concept of locally fine point, which is the generalized regular point, was introduced, many problems in nonlinear functional analysis have been solved, such as the conjugacy problem, the rank theorem in advanced calculus and so on. So locally fine point is a significant concept to take the place of regular points. In this paper, it is proved that the set of all of the locally fine points of f in U is also an open set in E .