한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제10권3호
  • /
  • Pages.193-198
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  • 2003
  • /
  • 1226-0657(pISSN)
  • /
  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지

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)
  • 발행 : 2003.08.01
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초록

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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