Universal Chord Theorem and a Topological Analysis

2026/01/20 by Ion Ciudin, Eugen J. Ionascu · 1 voice
Mathematics · #math.GN

paper · pdf

arxiv published 2026/01/20 · arxiv updated 2026/01/25

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.

Citations

• The horizontal chord set: to CIRM and back
• Average pace and horizontal chords

Discussions

• Ion Ciudin, Eugen J. Ionascu: Universal Chord Theorem and a Topological Analysis https://arxiv.org/abs/2601.14120 https://arxiv.org/pdf/2601.14120 https://arxiv.org/html/2601.14120 [bsky, 0 points, 0 comments]

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