on monotonic bijections on subgroups of r
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ID: 256995
2016
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Abstract
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
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| Reference Key |
buzyakova2016appliedon
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|---|---|
| Authors | ;Raushan Buzyakova |
| Journal | Health and quality of life outcomes |
| Year | 2016 |
| DOI |
10.4995/agt.2016.4116
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| URL | |
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