Uniqueness of completions and related topics
Functional Analysis
2018-02-27 v1 Metric Geometry
Abstract
A bounded subset of a normed linear space is said to be (diametrically) complete if it cannot be enlarged without increasing the diameter. A complete super set of a bounded set having the same diameter as is called a completion of . In general, a bounded set may have different completions. We study normed linear spaces having the property that there exists a nontrivial segment with a unique completion. It turns out that this property is strictly weaker than the property that each complete set is a ball, and it is strictly stronger than the property that each set of constant width is a ball. Extensions of this property are also discussed.
Keywords
Cite
@article{arxiv.1802.09133,
title = {Uniqueness of completions and related topics},
author = {Chan He and Horst Martini and Senlin Wu},
journal= {arXiv preprint arXiv:1802.09133},
year = {2018}
}