AI 中文总结
研究球面上函数水平集的内接正方形，利用连续函数性质，得出从\(S^2\)到\(\mathbb{R}\)的连续函数在\(S^2\)大圆内接正方形顶点取值相同的结论。
AI 中文摘要
每个从二维球面\(S^2\)到实数集\(\mathbb{R}\)的连续函数\(f\)，在\(S^2\)大圆内接正方形的顶点处取相同值。关键词：水平集、配置空间、施蒂费尔 - 惠特尼类、内接正方形、博苏克 - 乌拉姆型定理
英文摘要
According to a theorem by F.~Dyson, every continuous function $f: S^2 \to {\mathbb R}$ takes the same value at the vertices of a square inscribed into a great circle of $S^2$. We give a proof of this statement based on the theory of characteristic classes and indicate other potential applications of this approach.
