Discontinuity and Involutions on Countable Sets

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 $f:X\to X$ such that $f(f(x))=x$ for each $x\in X$ and $F$ is the set of discontinuity points of $f$.

The paper was published