Theorems · Theorem · complex analysis
MeromorphicOn.smul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {R : Type u_4} [inst_3 : NormedRing R] [inst_4 : Module R E] [IsBoundedSMul R E]
{U : Set 𝕜} [inst_6 : NormedAlgebra 𝕜 R] [IsScalarTower 𝕜 R E] {s : 𝕜 → R},
MeromorphicOn s U → ∀ {f : 𝕜 → E}, MeromorphicOn f U → MeromorphicOn (s • f) U- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- IsScalarTowerstatement and proof · cited by 3,896
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- IsBoundedSMulstatement and proof · cited by 329
- MeromorphicOnstatement and proof · cited by 141
- MeromorphicAt.smulproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- MeromorphicOn.divisor_smulproof · cited by 5
- MeromorphicOn.extract_zeros_polesproof · cited by 4
- MeromorphicOn.exists_canonicalDecompproof · cited by 1
- MeromorphicOn.fun_smulproof · cited by 0