非阿基米德n-赋范空间的等距  

Isometries on Non-Archimedean n-Normed Spaces

作　　者：马玉梅 王金芝 Ma Yumei;Wang Jinzhi(Department of Mathematics,Dalian Minzu Universityy Dalian 116600,China)

机构地区：[1]大连民族大学理学院数学系,辽宁大连116600

出　　处：《南开大学学报（自然科学版）》2022年第2期80-86,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：讨论非阿基米德n-赋范空间中的Mazur-Ulam定理和Aleksandrov问题.证明了非阿基米德n-赋范空间中的满的n-等距映射是反射的,并且保单位距离是等距的充要条件是其保持零-n-距离.The Mazur-Ulam theorem and the Aleksandrov problem are considered on non-Archimedean n-normed spaces. It’s proved that any surjective n-isometry between non-Archimedean n-normed spaces is affine;and a one-n-distance preserving mapping is an n-isometry if and only if it has zero-n-distance preserving property.

关 键 词：MAZUR-ULAM定理 Aleksandrov问题 非阿基米德n-赋范空间 n-等距 

分 类 号：O177[理学—数学]