论文标题
表征在封闭间隔的一类连续函数的级别集中点之间的距离
Characterizing Distances Between Points in the Level Sets of a Class of Continuous Functions on a Closed Interval
论文作者
论文摘要
给定连续函数$ f：[a，b] \ to \ mathbb {r} $，以至于$ f（a）= f（b）$，我们研究了一组距离$ | x-y | $ where $ f（x）= f（y）$。特别是，我们表明该集合必须包含的唯一距离是均匀分配$ [a，b] $的距离。此外，我们表明它必须至少包含间隔$ [0，b-a] $的三分之一。最后，我们探讨了一些更高的维度概括。
Given a continuous function $f:[a,b]\to\mathbb{R}$ such that $f(a)=f(b)$, we investigate the set of distances $|x-y|$ where $f(x)=f(y)$. In particular, we show that the only distances this set must contain are ones which evenly divide $[a,b]$. Additionally, we show that it must contain at least one third of the interval $[0,b-a]$. Lastly, we explore some higher dimensional generalizations.
