关键词: Isometry, p-normed space, Dopp

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