非阿基米德2-赋范空间的等距问题  

The Isometric Problem on Non-Archimedean 2-normed Spaces

作　　者：马玉梅 MA Yu - mei(School of Science, Dalian Minzu University, Dalian Liaoning 116605, China)

机构地区：[1]大连民族大学理学院,辽宁大连116605

出　　处：《大连民族大学学报》2017年第5期474-477,共4页Journal of Dalian Minzu University

基　　金：中央高校基本科研业务费专项资金资助项目(DC201502050301)

摘　　要：推广了Mazur-Ulam定理和Aleksbndrov问题到非阿基米德2-赋范空间。证明了两个非阿基米德空间的任何2-等距是仿射的;一个单位距离保持映射是2-等距当且仅当它保持零距离。This paper generalizes the Mazur-Ulam theorem and the Aleksandrov problem on non-Archimedean 2-normed spaces. It proves that any 2-isometric mapping between two non-Archimedean 2-normed spaces is affine; and a one-distance preserving mapping is 2-isometric if and only if it has zero-distance preserving property.

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

分 类 号：O177.3[理学—数学]