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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.10 No.3

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DISTANCE-PRESERVING MAPPINGS ON RESTRICTED DOMAINS

DISTANCE-PRESERVING MAPPINGS ON RESTRICTEDDOMAINS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2003, v.10 no.3, pp.193-198
Jung, Soon-Mo (Mathematics Section, College Of Science And Technology)
Lee, Ki-Suk (Department Of Mathematics Education, Korea National University Of Education)
Jung, Soon-Mo, & Lee, Ki-Suk. (2003). DISTANCE-PRESERVING MAPPINGS ON RESTRICTED DOMAINS, 10(3), 193-198.

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.

keywords
Aleksandrov problem, isometry, distance preserving mapping

한국수학교육학회지시리즈B:순수및응용수학

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