拟-β-n-空间上的n-等距  

n-Isometries in Quasi-β-n-Nomed Spaces

作　　者：张文怡 谭冬妮 黄旭剑 Zhang Wenyi;Tan Dongni;Huang Xujian(Department of Mathematics,College of Science,Tianjin University of Technology,Tianjiii 300384,China)

机构地区：[1]天津理工大学理学院数学系,天津300384

出　　处：《南开大学学报（自然科学版）》2021年第5期14-20,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the Project Funding of Innovation and Entrepreneurship for Undergraduates(201710060093)。

摘　　要：研究了拟-β-n-空间上的n-等距,并证明了此空间中的任意保n-距离1的满映射即是仿射等距.运用的主要工具是仿射几何中的基本定理.更进一步给出了拟-β-n-空间中刻画仿射n-等距的几条等价结论.n-isometries in quasi-β-n-normed spaces are studied and it’s shown that every surjective mapping preserving n-distance one is an affine n-isometry in such spaces.The main tools in this manuscript are the fundamental theorems of affine geometry.Moreover,some statements which are equivalent to characterizing mappings to be affine n-isometries in quasi-β-n-normed spaces are presented.

关 键 词：拟-β-n-空间 n-等距 共线性 

分 类 号：O177[理学—数学]