UNIT-CIRCLE-PRESERVING MAPPINGS

We prove that if a one‐to‐one mapping f : ℝ n → ℝ n ( n ≥ 2) preserves the unit circles, then f is a linear isometry up to translation.

Saved in:
Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2004, Vol.2004 (66), p.3577-3586-274
Main Authors: Jung, Soon-Mo, Kim, Byungbae
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that if a one‐to‐one mapping f : ℝ n → ℝ n ( n ≥ 2) preserves the unit circles, then f is a linear isometry up to translation.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171204404098