TY - JOUR
AU - Buzyakova, Raushan
PY - 2016/10/03
Y2 - 2023/06/04
TI - On monotonic bijections on subgroups of R
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 17
IS - 2
SE -
DO - 10.4995/agt.2016.4116
UR - https://polipapers.upv.es/index.php/AGT/article/view/4116
SP - 83-91
AB - 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
ER -