Theorems · Theorem · several complex variables
AnalyticAt.eventually_continuousAt
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
AnalyticAt 𝕜 f x → ∀ᶠ (y : E) in nhds x, ContinuousAt f y- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealproof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ContinuousAtstatement · cited by 697
- FormalMultilinearSeriesproof · cited by 615
- IsOpen.mem_nhdsproof · cited by 470
- AnalyticAtstatement and proof · cited by 321
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicAt.eventually_continuousAtproof · cited by 1