Charatonik, Włodzimierz J.; Samulewicz, Alicja; Wituła, Roman Limit sets in normed linear spaces. (English) Zbl 1365.54025 Colloq. Math. 147, No. 1, 35-42 (2017). Summary: 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 \(x_n\rightarrow 0\) 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. MSC: 54F15 Continua and generalizations 46B20 Geometry and structure of normed linear spaces 40A05 Convergence and divergence of series and sequences 40A25 Approximation to limiting values (summation of series, etc.) Keywords:normed space; limit point; series PDF BibTeX XML Cite \textit{W. J. Charatonik} et al., Colloq. Math. 147, No. 1, 35--42 (2017; Zbl 1365.54025) Full Text: DOI References: [1] pp. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.