关于Bünchen扩张定理的一个注记
A note on Brehm's extension theorem
摘要：
贝姆扩张定理指出，欧几里得空间的有限子集上的非可扩映射可以扩张为整个空间上的分段线性映射。本文证明了在有限子集由具有有理坐标的点组成的条件下，定理的证明是构造性的。此外，初始非可扩映射需要将具有有理坐标的点发送到具有有理坐标的点。二维的情况下被认为是。
英文摘要：
Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive provided that the finite subset consists of points with rational coordinates. Additionally, the initial non-expansive map needs to send points with rational coordinates to points with rational coordinates. The two-dimensional case is considered.
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。
