THE ALEKSANDROV PROBLEM FOR UNIT DISTANCE PRESERVING MAPPING

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