摘要
In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X 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 normed spaces was given. In addition, a proof which there doesn't exist any isometry between some spaces was obtained.
In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X 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 normed spaces was given. In addition, a proof which there doesn't exist any isometry between some spaces was obtained.
基金
NSF.
