International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 65-68, Pages 3577-3586
doi:10.1155/S0161171204404098
Unit-circle-preserving mappings
Soon-Mo Jung
and Byungbae Kim
Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, Korea
Abstract
We prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation.