Theorems · Theorem · complex analysis
MeromorphicOn.eventually_analyticAt_or_mem_compl
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜} {U : Set 𝕜},
MeromorphicOn f U → x ∈ U → ∀ᶠ (y : 𝕜) in nhdsWithin x {x}ᶜ, AnalyticAt 𝕜 f y ∨ y ∈ Uᶜ- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterproof · cited by 8,121
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- Set.extproof · cited by 2,266
- nhdsWithinstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- AnalyticAtstatement and proof · cited by 321
Cited by3
Results whose statement or proof uses this declaration.
- MeromorphicOn.analyticAt_mem_codiscreteWithinproof · cited by 7
- MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNEproof · cited by 3
- MeromorphicOn.codiscrete_setOfPred_meromorphicOrderAt_eq_zero_or_topproof · cited by 2