开映射和空间的完全完备性  

The Complete Completeness of Open Mapping and Space

作　　者：边红[1] 裘重宜 于海征[2] BIAN Hong;QIU Chongyi;YU Haizheng(Department of Mathematics and System Sciences,Xinjiang Normal University,Urumqi Xinjiang 830017,China;School of Mathematics,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2020年第2期134-136,共3页Journal of Xinjiang University(Natural Science Edition)

基　　金：国家自然科学基金(11761070,61662079);新疆师范大学“十三五”校级重点学科数学资助(17SDKD11).

摘　　要：本文的目的是对已有的定理"从局部凸空间E到任意局部凸空间上的连续的几乎开的线性映射总为开映射时,E是全完备的"给出一种新的证明方法.在分离的局部凸空间的条件下,利用连续的开线性映射的共轭映射的值域是弱闭的性质,证明了如下结论:若E是分离的局部凸空间,且从E到任意一个局部凸空间上的连续的几乎开的线性映射是开映射,则E是全完备的.In this paper,we aim to present a new proof for the Theorem:if the continuous and almost open linear mapping from the local convex space E to arbitrary local convex space is always open mapping,then E is complete completeness.Under the condition of separated locally convex space,making use of the properties that the range of conjugate mappings of continuous open linear mappings is weakly closed,we prove that if E is separated locally convex space,and the continuous and almost open linear mapping from the local convex space E to arbitrary local convex space is always open mapping,then E is complete completeness.

关 键 词：开映射 全完备空间 商映射 共轭映射的值域 

分 类 号：O177.92[理学—数学]