Theorems · Theorem · complex analysis
MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt
∀ {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}, MeromorphicAt f x → f =ᶠ[nhdsWithin x {x}ᶜ] toMeromorphicNFAt f xConversion to normal form at x changes the value only at x.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 200 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 · 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
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Filter.EventuallyEqstatement · cited by 1,912
- MeromorphicAtstatement and proof · cited by 160
- eventually_nhdsWithin_of_forallproof · cited by 18
- toMeromorphicNFAtstatement · cited by 15
- MeromorphicAt.eqOn_compl_singleton_toMeromorphicNFAtproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- meromorphicNFAt_toMeromorphicNFAtproof · cited by 5
- MeromorphicAt.meromorphicOrderAt_toMeromorphicNFAtproof · cited by 2
- toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhdsproof · cited by 2
- toMeromorphicNFAt_eventuallyEq_nhds_congrproof · cited by 1
- MeromorphicAt.toMeromorphicNFAt_eventuallyEq_nhds_iffproof · cited by 0