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arXiv · 0705.2109

Discontinuity and Involutions on Countable Sets

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

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Sung Soo Kim, Szymon Plewik. 2007-05-15. Discontinuity and Involutions on Countable Sets. https://arxiv.org/abs/0705.2109

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