关于欧几里得空间的刚性代数结构
On the rigid algebraic structure of Euclidean spaces
摘要：
证明了欧几里得空间的自同构群与相应分解的算术空间的拓扑自同构群同构。特别地，具有正签名的欧几里德n-空间的几何与n维算术空间到n维球面的因式分解相关联。
英文摘要：
It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular, the geometry of Euclidean n-space with positive signature is associated with factorization of n-dimensional arithmetic space into n-dimensional sphere.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
