Characterizing distances between points in the level sets of a class of continuous functions on a closed interval
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.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Mathematical Dynamics and Fractals
Mathematics and Applications
Publication details
- Journal / source
- Mathematics Exchange
- Volume
- 17
- Issue
- 1
- Pages
- 49–58
- Publication date
- 3 March 2026
- Language
- EN