Theorems · Theorem · several complex variables
analyticWithinAt_univ
∀ {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},
AnalyticWithinAt 𝕜 f Set.univ x ↔ AnalyticAt 𝕜 f x- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univstatement · cited by 3,945
- FormalMultilinearSeriesproof · cited by 615
- AnalyticAtstatement · cited by 321
- AnalyticWithinAtstatement · cited by 96
- HasFPowerSeriesAtproof · cited by 94
Cited by9
Results whose statement or proof uses this declaration.
- AnalyticAt.compproof · cited by 28
- AnalyticAt.analyticWithinAtproof · cited by 19
- ContDiffAt.analyticAtproof · cited by 11
- AnalyticAt.comp_analyticWithinAtproof · cited by 10
- AnalyticAt.powproof · cited by 9
- AnalyticAt.contDiffAtproof · cited by 8
- HasFPowerSeriesOnBall.analyticAt_of_memproof · cited by 5
- AnalyticAt.cpowproof · cited by 1
- AnalyticAt.aeval_polynomialproof · cited by 1