超空间上的连续对应与对应的闭图

本文的目的是在超空间上重新定义上半连续,下半连续和连续对应．改进了Ｋｌｅｉｎ在［１］中的定义７．１．１,得到了这些对应和它们的闭图的若干特征和性质,给出了子集网在下半连续对应中的应用     

关于半自反空间的一个闭图定理

本文给出了一个关于半自反ｉｎｆｒａ－（ｕ）空间的闭图定理．作为推论,证明了从速完备 Ｍａｚｕｒ空间到半自反ｉｎｆｒａ－（ｕ）空间的闭图线性映照为弱连续、Ｍａｃｋｅｙ连续和强连续的．     

Some Properties of Two Kinds of Multifunctions

Let X and Y be metrizable topological linear spaces.In this paper,the following results are proved:(1)If X and Y are complete,F;X→Y is a point closed u.s.c.,and symmetric process with ——↑F(X)=Y,then either F(X) is meager in Y,or else F is an open multifunction with F(X)=Y.(2)If X is complete,and F:X→Y is a process with a subclosed graph,then F is l.s.c..We also discuss topological multi-homomorphisms between topological linear spaces.     

AN IMPROVED NONLINEAR CLOSED GRAPH THEOREM

In this paper, a new nonlinear closed graph theorem is established, whose result improves substantially a recent-known important conclusion.     

一类闭图定理

设(A)空间类是 Mackey 空间类的子类且具有关于 Hausdorff 商的承继性,称局部凸空间(F,η)为 C(A)空间若它满足:对于 F 的任何线性子空间 M 及 M~# 的任何线性子空间 N,若对偶双(M,N)为(A)形的且集合{y′∈F′:y′|_M∈N}分离 F 中点,则必有:(?)y′∈F′,y′|_M∈N.我们证明了如下相当一般的闭图定理:从任何(A)空间到局部凸空间(F,η)中的闭图线性映照为连续的充要条件是:(F,η)为 C(A)空间.由此推出一类闭图定理,这其中包括了著名的 Pták 闭图定理和 Kalton 闭图定理的完全推广.     

Robinson－Ursescu Theorem in p－normed Spaces

For a convex set-valued map between p-normed (0 < p ≤ 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.     

超空间上的连续对应与对应的闭图

本文的目的是在超空间上重新定义上半连续,下半连续和连续对应.改进了Klein在［1］中的定义7.1.1,得到了这些对应和它们的闭图的若干特征和性质,给出了子集网在下半连续对应中的应用.