赋准范空间中几种有界性讨论  

The boundedness,norm-bounded and pseudobounded of F~*-space

作　　者：董立华[1] 王俊青[2] 姜曰华[1] 

机构地区：[1]德州学院数学系,山东德州253023 [2]天津工业大学理学院,天津300160

出　　处：《纺织高校基础科学学报》2004年第2期116-118,共3页Basic Sciences Journal of Textile Universities

摘　　要：E中集M的有界性是指对于趋于0的任何数列{εn}以及任何元列{xn} M,均有εnxn→0　(n→∞),由此证明了赋准范空间中集M的有界性蕴涵按准范有界和拟有界性,并通过例子说明了两个结论的逆是不成立的,最后给出拟有界集性质的应用.Boundedness of a set M in E is that,for any a sequence of number {ε_n} and any a sequence of element {x_n}M,it holds that ε_nx_n→0(n→∞).By this ,it is proved that boundedeness of a set M in a quasinormed space turns out its boundedness by quasinorme and quasiboundedness,and with a contrary example,it is stated that inverses of the two conclusions don't hold.Finally,application of properties of a quasibounede set is given.

关 键 词：赋准范空间 有界性 按范有界 拟有界PB-B 

分 类 号：O17[理学—数学]