The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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DISTANCE-PRESERVING MAPPINGS ON RESTRICTED DOMAINS

  • Jung, Soon-Mo (Mathematics Section, College Of Science And Technology) ;
  • Lee, Ki-Suk (Department Of Mathematics Education, Korea National University Of Education)
  • Published : 2003.08.01
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Abstract

Let X and Y be n-dimensional Euclidean spaces with $n\;{\geq}\;3$. In this paper, we generalize a classical theorem of Bookman and Quarles by proving that if a mapping, from a half space of X into Y, preserves a distance $\rho$, then the restriction of f to a subset of the half space is an isometry.

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