LIMIT SETS IN NORMED LINEAR SPACES

被引：1
|
作者：
Charatonik, Wlodzimierz J. [1 ]
Samulewicz, Alicja [2 ]
Witula, Roman [2 ]
机构：
[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA
[2] Silesian Tech Univ, Fac Appl Math, Inst Math, Kaszubska 23, PL-44101 Gliwice, Poland
来源：
COLLOQUIUM MATHEMATICUM | 2017年 / 147卷 / 01期
关键词：
normed space; limit point; series; VECTOR SERIES; REARRANGEMENTS; THEOREM;
D O I：
10.4064/cm6868-5-2016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The sets of all limit points of series with terms tending to 0 in normed linear spaces are characterized. An immediate conclusion is that a normed linear space (X, parallel to.parallel to) is infinite-dimensional if and only if there exists a series Sigma x(n) of terms of X with x(n) -> 0 whose set of limit points contains exactly two different points of X. The last assertion could be extended to an arbitrary (greater than 1) finite number of points.
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页码：35 / 42
页数：8
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