The horizontal chord set: to CIRM and back

2023/03/22 by Davis, Diana, Troubetzkoy, Serge · 1 citation
#26A15 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2303.12820

Abstract

We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf's characterization of this set, and show that it implies that no matter which function we choose, at least half of the possible lengths occur. We prove several results about functions for which all the possible lengths occur.

Cited by

• Universal Chord Theorem and a Topological Analysis

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