闭曲线之间的最优同胚
Optimal homeomorphisms between closed curves
摘要：
自然伪距离的概念已被证明是一个强有力的工具，用于衡量拓扑空间之间的不相似赋予连续实值函数。粗略地说，自然伪距离被定义为函数值变化的下确界，如果可能的话，通过同胚从一个空间移动到另一个空间。本文证明了关于闭曲线之间存在最优同胚的第一个结果，即引起函数的变化等于自然伪距离。
英文摘要：
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance.
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。
