On monotonic bijections on subgroups of R

• Autores: Raushan Z. Buzyakova
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 17, Nº. 2, 2016, págs. 83-91
• Idioma: inglés
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• Resumen

  • 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