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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 2508172, 3 pages
http://dx.doi.org/10.1155/2016/2508172
Research Article

More of Dedekind: His Series Test in Normed Spaces

1Department of Mathematics, Hamilton College, 198 College Hill Road, Clinton, NY 13323, USA
2Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Received 6 December 2015; Accepted 5 May 2016

Academic Editor: Attila Gilányi

Copyright © 2016 Robert Kantrowitz and Michael M. Neumann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Dedekind’s test for infinite series has a canonical interpretation in the context of normed spaces. It is shown that his test holds in a normed space precisely when the space is complete.