完成的唯一性和相关主题
Uniqueness of completions and related topics
摘要：
一个赋范线性空间的有界子集被称为（直径）完备的，如果它不能在不增加直径的情况下扩大。有有界集$K$的完备超集与$K$具有相同的直径，称为$K$的完备化。一般来说，一个有界集可以有不同的完备化。我们研究赋范线性空间的性质，存在一个非平凡的部分，一个唯一的完成。事实证明，这个性质严格弱于每个完备集是球的性质，而严格强于每个恒定宽度集是球的性质。本文还讨论了这一性质的推广。
英文摘要：
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 $K$ having the same diameter as $K$ is called a completion of $K$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
