Subsum Sets: Intervals, Cantor Sets, and Cantorvals
History and Overview
2013-07-09 v2 Classical Analysis and ODEs
General Topology
Abstract
Given a sequence converging to zero, we consider the set of numbers which are sums of (infinite, finite, or empty) subsequences. When the original sequence is not absolutely summable, the subsum set is an unbounded closed interval which includes zero. When it is absolutely summable the subsum set is one of the following: a finite union of (nontrivial) compact intervals, a Cantor set, or a "symmetric Cantorval".
Cite
@article{arxiv.1106.3779,
title = {Subsum Sets: Intervals, Cantor Sets, and Cantorvals},
author = {Zbigniew Nitecki},
journal= {arXiv preprint arXiv:1106.3779},
year = {2013}
}
Comments
24 pages, 2 figures; replaces previous version (1106.3779) with different title (The subsum set of a null sequence), rewritten to shorten and take account of results not included in earlier version