continuous, monotonic, bijective

[gusl]

There should be a single adjective to describe transformations f : R -> R that are continuous, monotonic, bijective. (sorta equivalent to the condition: f' is continuous, zero nowhere, and not converging to zero too quickly... I say "sorta" because f(x) = x^3 violates the "zero nowhere" condition)

(tangentially, I'm fairly confident that they form a group under composition, with the increasing functions as a subgroup)