# Discontinuity and Involutions on Countable Sets - Mathematics > General Mathematics

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Abstract: For any infinite subset $X$ of the rationals and a subset $F \subseteq X$which has no isolated points in $X$ we construct a function $f: X \to X$ suchthat $f(f(x))=x$ for each $x\in X$ and $F$ is the set of discontinuity pointsof $f$.

Autor: Sung Soo Kim, Szymon Plewik

Fuente: https://arxiv.org/