半拓扑线性空间及其性质(Ⅱ)  

Semi-Topological Linear Spaces and Its Properties(Ⅱ)

作　　者：吴大勇[1] 苏雅拉图[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《甘肃联合大学学报（自然科学版）》2009年第2期23-26,30,共5页Journal of Gansu Lianhe University :Natural Sciences

基　　金：内蒙古自然科学基金资助项目(200508010106)

摘　　要：我们在文[9]引入了半拓扑线性空间的概念,并得到了半拓扑线性空间中半开集、半闭包、半内部、S邻域、局部S-基等方面的一些基本结果.本文进一步讨论了半拓扑线性空间的性质,得到了如下结果:(1)证明了半拓扑线性空间中凸集的半闭包和半内部均为凸集;半拓扑线性空间中平衡集的半闭包是,平衡集,并且当平衡集的半内部包含0点时,平衡集的半内部也是平衡集;在半拓扑线性空间中存在着由半闭的平衡集构成的0点的局部S-基.(2)证明了半拓扑线性空间中半拓扑线性有界集的子集是半拓扑线性有界的,有限个半拓扑线性有界集的并集也是半拓扑线性有界的,S-紧集是半拓扑线性有界的.(3)对具有C性质的半拓扑线性空间,证明了半拓扑线性有界集的半闭包是半拓扑线性有界的,有限个半拓扑线性有界集的和是半拓扑线性有界的.(4)对具有C性质的半拓扑线性空间,证明了α集A是S-紧集当且仅当A是完全半拓扑线性有界的S-完备集.We introduced the definition of semi-toplogical linear spaces in paper[9],and obtained some fundamental result of semi-open sets, semi-closure set, semi-interior, local S-base. Furthermore in this paper,we discusses the properties of semi-topological linear spaces, following results are got：（1） semi-closure and semi-inteior of convex sets are both convex sets in semi-topological linear spaces, the semi-closure of balanced sets in semi-topological linear spaces are balanced sets and semi-inteior of balanced sets are balanced sets, semi-inteior of balanced sets contained zero point is balanced sets; （2） subset of STL-bounded sets is STL-bounded sets, limited union STL-bounded sets is STL-bounded sets, S-compact sets are STL-bounded sets; （3）for semi-topological linear spaces with C- properties, we prove that the semi-closure of STL-bounded sets is STL-bounded sets and sum of limited STL- bounded sets is STL-bounded sets; （4） for semi-topological linear spaces with C- properties, we also prove that a -set A is S -compact sets if and only A is finite STL-bounded sets and S-complet sets.

关 键 词：半开集 半拓扑线性空间 STL有界 S-紧集 

分 类 号：O177.3[理学—数学]