Theorems · Theorem · dynamical systems
Function.Commute.right_bijOn_fixedPoints_comp
∀ {α : Type u_1} {f g : α → α},
Function.Commute f g → Set.BijOn g (Function.fixedPoints (f ∘ g)) (Function.fixedPoints (f ∘ g))If self-maps f and g commute, then g is bijective on the set of fixed points of f ∘ g.
This is a particular case of Function.bijOn_fixedPoints_comp.
- Defined in
- Mathlib.Dynamics.FixedPoints.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Quot.sound
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Cites5
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- Set.BijOnstatement and proof · cited by 168
- Function.fixedPointsstatement and proof · cited by 90
- Function.Commutestatement and proof · cited by 54
- Function.Semiconj.comp_eqproof · cited by 11
- Function.bijOn_fixedPoints_compproof · cited by 2
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