Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (3): 359-364.

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THE ALEKSANDROV PROBLEM FOR UNIT DISTANCE PRESERVING MAPPING

 MA Yu-Mei   

  1. Department of Mathematics, Dalian University, Dalian 116622, China
  • Received:1998-07-03 Revised:1999-07-07 Online:2000-05-20 Published:2000-05-20
  • Supported by:

    This work supported by NSF. e-mail: mawenjia263.net

Abstract:

In this paper, one of the Aleksandrov problem was resolved, the proof thata
mapping f which preserve unit distance between two real p-normed spacesX and Y is an
isometry if Y is a p-strictly convex space and f satisfies locally Lipschitz condition was
shown, and a same result in normedspaces was given. In addition, a proof which there
doesn’t exist any isometry between some spaces was obtained.

Key words: Isometry, p-normed space, Dopp

CLC Number: 

  • 46B04
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