Uniqueness of completions and related topics

作者：He, Chan^*; Martini, Horst; Wu, Senlin

来源：ARCHIV DER MATHEMATIK, 2018, 111(2): 157-165.

DOI：10.1007/s00013-018-1177-x

• Banach spaces
• Completeness
• Constant width set
• Normed linear space
• Uniqueness of completion

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.

• 出版日期2018-8
• 单位中北大学