Optimal homeomorphisms between closed curves
Differential Geometry
2009-06-26 v1
Abstract
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.
Cite
@article{arxiv.0906.4648,
title = {Optimal homeomorphisms between closed curves},
author = {Andrea Cerri and Barbara Di Fabio},
journal= {arXiv preprint arXiv:0906.4648},
year = {2009}
}
Comments
11 pages, 3 figures