Theorems · Theorem · functional analysis
NormedSpace.map_exp_of_mem_ball
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} {𝔹 : Type u_3} [inst : NontriviallyNormedField 𝕂] [inst_1 : NormedRing 𝔸]
[inst_2 : NormedRing 𝔹] [inst_3 : NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸] [Algebra 𝕂 𝔹] [CharZero 𝕂] {F : Type u_4}
[inst_7 : FunLike F 𝔸 𝔹] [RingHomClass F 𝔸 𝔹] (f : F),
Continuous ⇑f → ∀ x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius, f (NormedSpace.exp x) = NormedSpace.exp (f x)Any continuous ring homomorphism commutes with NormedSpace.exp.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Continuousstatement and proof · cited by 2,592
- FunLikestatement and proof · cited by 2,560
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalproof · cited by 2,068
- NormedAlgebrastatement and proof · cited by 1,165
- tsumproof · cited by 1,148
- CharZerostatement and proof · cited by 932
- NormedRingstatement and proof · cited by 924
Cited by2
Results whose statement or proof uses this declaration.
- NormedSpace.map_expproof · cited by 7
- NormedSpace.algebraMap_exp_comm_of_mem_ballproof · cited by 1