Theorems · Theorem · complex analysis
MeromorphicOn.codiscrete_setOfPred_meromorphicOrderAt_eq_zero_or_top
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜},
MeromorphicOn f U → {u | meromorphicOrderAt f ↑u = 0 ∨ meromorphicOrderAt f ↑u = ⊤} ∈ Filter.codiscrete ↑UThe set where a meromorphic function has zero or infinite order is codiscrete within its domain of meromorphicity.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- WithTopstatement · cited by 3,754
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
Cited by2
Results whose statement or proof uses this declaration.
- MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_topproof · cited by 0