Theorems · Theorem · several complex variables
analyticAt_inv
∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {𝕝 : Type u_8} [inst_1 : NormedDivisionRing 𝕝]
[inst_2 : NormedAlgebra 𝕜 𝕝] {z : 𝕝}, z ≠ 0 → AnalyticAt 𝕜 Inv.inv zIf 𝕝 is a normed field extension of 𝕜, then the inverse map 𝕝 → 𝕝 is 𝕜-analytic
away from 0.
- Defined in
- Mathlib.Analysis.Analytic.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 190 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.
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Units.valproof · cited by 1,966
- NormedAlgebrastatement and proof · cited by 1,165
- NormedDivisionRingstatement and proof · cited by 360
- AnalyticAtstatement and proof · cited by 321
- Units.mk0proof · cited by 181
- Ring.inverseproof · cited by 160
- Ring.inverse_eq_inv'proof · cited by 15
- analyticAt_inverseproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- AnalyticAt.invproof · cited by 13
- AnalyticWithinAt.invproof · cited by 4
- analyticOnNhd_invproof · cited by 1