Universal Chord Theorem and a Topological Analysis
General Topology
2026-01-27 v2
Abstract
We study the set of chords of a real-valued continuous function on [0,1] with f(0)=f(1)=0. We describe which chords may appear as isolated points and provide examples illustrating our characterization. Maximal Hopf sets are introduced and analyzed.
Cite
@article{arxiv.2601.14120,
title = {Universal Chord Theorem and a Topological Analysis},
author = {Ion Ciudin and Eugen J. Ionascu},
journal= {arXiv preprint arXiv:2601.14120},
year = {2026}
}
Comments
9 pages, 5 figures