Theorems · Theorem · Lie groups
ContinuousOn.fun_pow
∀ {M : Type u_3} {X : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace M] [inst_2 : Monoid M]
[ContinuousMul M] {f : X → M} {s : Set X}, ContinuousOn f s → ∀ (n : ℕ), ContinuousOn (fun i => f i ^ n) sEta-expanded form of ContinuousOn.pow
- Defined in
- Mathlib.Topology.Algebra.Monoid
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- Monoidstatement · cited by 3,887
- ContinuousOnstatement · cited by 1,411
- ContinuousMulstatement · cited by 343
- ContinuousOn.powproof · cited by 4
Cited by15
Results whose statement or proof uses this declaration.
- cfc_powproof · cited by 8
- Real.sin_gt_sub_cubeproof · cited by 2
- Real.tendstoLocallyUniformlyOn_rpow_sub_one_logproof · cited by 2
- ModularForm.multipliableLocallyUniformlyOn_one_sub_powproof · cited by 2
- multipliableUniformlyOn_euler_sin_prod_on_compactproof · cited by 1
- CStarAlgebra.pow_antitoneproof · cited by 1
- ZetaAsymptotics.term_oneproof · cited by 1
- cfc_map_polynomialproof · cited by 1
- cfcUnits_powstatement and proof · cited by 1
- cfc_comp_powproof · cited by 0
- CStarAlgebra.pow_monotoneproof · cited by 0
- CFC.log_powproof · cited by 0