Limit Sets in Normed Linear Spaces

Author

W. J. Charatonik, Missouri University of Science and TechnologyFollow
Alicja Samulewicz
Roman Witula

Abstract

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 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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

Limit point; Normed space; Series

International Standard Serial Number (ISSN)

0010-1354

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Language 2

Polish

Rights

© 2017 Instytut Matematyczny, All rights reserved.

Publication Date

01 Jan 2017