The scaling map ψ_α on the complexity quasi-metric space is expansive if and only if α ≠ 1, with its δ-stable sets coinciding exactly with asymptotic complexity classes.
Cobzaş, Functional Analysis in Asymmetric Normed Spaces , Frontiers in Mathematics, Birkhäuser/Springer, 2013
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Expansive homeomorphisms on complexity quasi-metric spaces
The scaling map ψ_α on the complexity quasi-metric space is expansive if and only if α ≠ 1, with its δ-stable sets coinciding exactly with asymptotic complexity classes.