Limit Sets in Normed Linear Spaces
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, || · ||) is infinite-dimensional if and only if there exists a series Σ xn of terms of X with xn → 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.
W. J. Charatonik et al., "Limit Sets in Normed Linear Spaces," Colloquium Mathematicum, vol. 147, no. 1, pp. 35-42, Instytut Matematyczny, Jan 2017.
The definitive version is available at https://doi.org/10.4064/cm6868-5-2016
Mathematics and Statistics
Keywords and Phrases
Limit point; Normed space; Series
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2017