Characterizing distances between points in the level sets of a class of continuous functions on a closed interval

Authors

  • Henry Riely Kennesaw State University
  • Yuanming Luo Georgia Institute of Technology

DOI:

https://doi.org/10.33043/yB4457yFCQ

Abstract

Given a continuous function f : [a,b] → R such that f(a) = f(b), we investigate the set of distances |x−y| where f(x) = f(y). In particular, we show that the only distances this set must contain are ones which evenly divide [a,b]. Additionally, we show that it must contain at least one third of the interval [0,b−a]. Lastly, we explore some higher dimensional generalizations.

Author Biographies

Henry Riely, Kennesaw State University

Henry Riely received his Ph.D. from the Washington State University in 2019. He is a lecturer at Kennesaw State University. His main mathematical interests lie in analysis, especially stochastic processes and harmonic analysis.

Yuanming Luo, Georgia Institute of Technology

Yuanming Luo is a junior undergraduate student at Georgia Institute of Technology. He is working toward both math and computer science degrees. His primary research interests are partial differential equations and numerical methods.

References

Abbott, Stephen, Understanding Analysis, Undergraduate Texts in Mathematics, Springer, New York, 2015.

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Published

2026-03-03

How to Cite

Riely, H., & Luo, Y. (2026). Characterizing distances between points in the level sets of a class of continuous functions on a closed interval. Mathematics Exchange, 17(1), 49–58. https://doi.org/10.33043/yB4457yFCQ

Issue

Vol. 17 No. 1 (2023): Mathematics Exchange, Fall 2023

Section

Articles

License

Copyright (c) 2026 Henry Riely, Yuanming Luo

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.