赋准范空间中序列x_(n_m)~r_(n_m+p)审敛原理  

The convergence principle for the sequence x_(n_m)~r_(n_m+p) in pre-normed spaces

作　　者：倪培溉[1] 陶志[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《中国科学技术大学学报》2008年第5期488-490,共3页JUSTC

基　　金：国家自然科学基金委员会与中国民用航空总局联合资助项目(60672178)资助

摘　　要：给出了赋准范空间中序列xnm^rnm+p审敛原理,该审敛原理是赋准范空间中序列柯西审敛原理的等价命题.在赋准范空间中利用该审敛原理判别序列的敛散性比利用柯西审敛原理更简单快捷,可以对以往的判别序列收敛性的判别法进行推广.The convergence principle for the sequence xnm～rnm＋p in pre-normed spaces was obtained, which was an equivalent proposition of Cauchy＇s convergence principle for sequences in pre-normed spaces. This convergence principle is simpler and faster than Cauchy＇s convergence principle in judging the convergence for sequences in pre-normed spaces. Using the convergence principle for the sequence xnm～rnm＋pin prenormed spaces, the scope of application of the previous methods for convergence judgement can be expanded.

关 键 词：拓扑线性空间 赋准范空间 To公理 A1公理 

分 类 号：O177[理学—数学]