@article{Buzyakova_2016, title={On monotonic bijections on subgroups of R}, volume={17}, url={https://polipapers.upv.es/index.php/AGT/article/view/4116}, DOI={10.4995/agt.2016.4116}, abstractNote={We show that for any continuous monotonic bijection $f$ 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 a periodic-point free continuous bijections. We explore a few routes leading to generalizations and counterexamples}, number={2}, journal={Applied General Topology}, author={Buzyakova, Raushan}, year={2016}, month={Oct.}, pages={83–91} }