Geodesic
Limit sets in normed linear spaces
Włodzimierz J. Charatonik 1   ; Alicja Samulewicz 2   ; Roman Wituła 2
1 Department of Mathematics and Statistics Missouri University of Science and Technology Rolla, MO 65409, U.S.A.
2 Institute of Mathematics Faculty of Applied Mathematics Silesian University of Technology Kaszubska 23 44-101 Gliwice, Poland
Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 35-42 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $(X,\| \cdot \| )$ is infinite-dimensional if and only if there exists a series $\sum x_n$ of terms of $X$ with $x_n\to 0$ 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.
DOI : 10.4064/cm6868-5-2016
Keywords: sets limit points series terms tending normed linear spaces characterized immediate conclusion normed linear space cdot infinite dimensional only there exists series sum terms whose set limit points contains exactly different points assertion could extended arbitrary greater finite number points

Włodzimierz J. Charatonik  1   ; Alicja Samulewicz  2   ; Roman Wituła  2

1 Department of Mathematics and Statistics Missouri University of Science and Technology Rolla, MO 65409, U.S.A.
2 Institute of Mathematics Faculty of Applied Mathematics Silesian University of Technology Kaszubska 23 44-101 Gliwice, Poland 
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Włodzimierz J. Charatonik; Alicja Samulewicz; Roman Wituła. Limit sets in normed linear spaces. Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 35-42. doi: 10.4064/cm6868-5-2016

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