关于格点反问题的一个注记
A note on the inverse problem for the lattice points
摘要：
设$K\subseteq\mathbb{R}^2$是紧集，使得$K+\mathbb{Z}^2=\mathbb{R}^2$ .利用代数拓扑的方法证明了$K$的差集$(K-K)\cap\mathbb{Z}^2$的整数点不包含在坐标轴$\mathbb{Z}\times\{0\}\cup\mathbb{Z}\times\{0\}$上。这一结果否定了Hegarty和M. Nathanson关于互素格点的一个推广.
英文摘要：
Let $K\subseteq\mathbb{R}^2$ be a compact set such that $K+\mathbb{Z}^2=\mathbb{R}^2$. We prove, via Algebraic Topology, that the integer points of the difference set of $K$, $(K-K)\cap\mathbb{Z}^2$, is not contained on the coordinate axes, $\mathbb{Z}\times\{0\}\cup\mathbb{Z}\times\{0\}$. This result gives a negative answer to a question posed by P. Hegarty and M. Nathanson on relatively prime lattice points.
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。
