n-赋范空间上的等距延拓问题  

ISometric Extension on N-normed Spaces

作　　者：马玉梅 MA Yu-mei(School of Science, Dalian Minzu University, Dalian Liaoning 116650, China)

机构地区：[1]大连民族大学理学院,辽宁大连116650

出　　处：《大连民族大学学报》2021年第5期422-426,共5页Journal of Dalian Minzu University

摘　　要：给出了n-赋范空间中保持单位距离映射的性质以及其与2共线、保持零距离的关系。推广了Benz定理,证明了n-赋范空间之间保持两个常数距离的映射必为仿射等距。This paper gives the properties of the mapping that preserve the unit distance,and the relations to being the 2-colinear and preserving the zero distance.It generalized Benz theorem and proved that the mapping between the n-normed spaces which preserving two constant number distances was necessarily an affine isometry.

关 键 词：Aleksandrov问题 等距 n-赋范空间 Benz定理 

分 类 号：O172.2[理学—数学]