Theorems · Theorem · several complex variables
hasFPowerSeriesWithinAt_iff_of_nhds
∀ {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] {x : E} (f : E → F)
(p : FormalMultilinearSeries 𝕜 E F) {U : Set E},
U ∈ nhds x → (HasFPowerSeriesWithinAt f p U x ↔ HasFPowerSeriesAt f p x)- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.univproof · cited by 3,945
- FormalMultilinearSeriesstatement and proof · cited by 615
- Set.subset_univproof · cited by 228
- HasFPowerSeriesAtstatement · cited by 94
- HasFPowerSeriesWithinAtstatement and proof · cited by 53
- mem_nhdsWithin_of_mem_nhdsproof · cited by 50
Cited by1
Results whose statement or proof uses this declaration.
- AnalyticOn.analyticAtproof · cited by 0