局部p-凸空间中的p-滴状定理(英文)

A p-drop theorem in locally p-convex spaces

给出局部p-凸空间(0＜p＜1)中的p-滴状定理如下：设X为局部完备局部p-凸空间,A(?)X为局部闭集且B(?)X为局部闭,有界,p-凸集。若存在一个p-凸吸收集W使W∩(A-B)=(?),则对于任意x_0∈A,存在a∈D_p(x_0,B)∩A使得D_p(a,B)∩A={a}。

A p-drop theorem in locally p-convex（ 0＜ p ＜ 1）spaces is given as follows. Let X be a locally complete locally p-convex spaoe,A（∪）X be a locally closed set and B（∪）X be a locally closed,bounded, p-convex set. If there exists a p-convex absorbing set W such that W∩ （A - B） = （φ）,then for any x0∈A,there exitsts a ∈ Dp（x0,B） ∩A such that Dp（a ,B） ∩ A={a}.