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arXiv · 1606.05311

On Monotonic Fixed-Point Free Bijections on Subgroups of $\mathbb R$

Raushan Buzyakova
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Abstract

We show that for any continuous monotonic fixed-point free automorphism $f$ on a $\sigma$-compact subgroup $G\subset \mathbb R$ there exists a binary operation $+_f$ such that $\langle G, +_f\rangle$ is a topological group topologically isomorphic to $\langle G, +\rangle$ and $f$ is a shift with respect to $+_f$. We then show that monotonicity cannot be replaced by the property of being periodic-point free. We explore a few routes leading to generalizations and counterexamples.

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BibTeXRIS

Raushan Buzyakova. 2016-06-16. On Monotonic Fixed-Point Free Bijections on Subgroups of $\mathbb R$. https://arxiv.org/abs/1606.05311

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