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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.10 No.3

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DISTANCE-PRESERVING MAPPINGS ON RESTRICTEDDOMAINS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2003, v.10 no.3, pp.193-198
Jung, Soon-Mo
Lee, Ki-Suk
Jung,, S. , & Lee,, K. (2003). DISTANCE-PRESERVING MAPPINGS ON RESTRICTEDDOMAINS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 10(3), 193-198.

Abstract

Let X and Y be n-dimensional Euclidean spaces with <TEX>$n\;{\geq}\;3$</TEX>. 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 <TEX>$\rho$</TEX>, then the restriction of f to a subset of the half space is an isometry.

keywords
Aleksandrov problem, isometry, distance preserving mapping

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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