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Theorems · Theorem · several complex variables

analyticOnNhd_inv

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {𝕝 : Type u_8} [inst_1 : NormedDivisionRing 𝕝]
  [inst_2 : NormedAlgebra 𝕜 𝕝], AnalyticOnNhd 𝕜 (fun z => z⁻¹) {z | z ≠ 0}

x⁻¹ is analytic away from zero

Defined in
Mathlib.Analysis.Analytic.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedDivisionRingNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

analyticOn_inv · cited by 0analyticOn_invNontriviallyNormedField · cited by 8742NontriviallyNormedFieldSet.ofPred · cited by 6101Set.ofPredNormedAlgebra · cited by 1165NormedAlgebraNormedDivisionRing · cited by 360NormedDivisionRingAnalyticOnNhd · cited by 206AnalyticOnNhdanalyticAt_inv · cited by 3analyticAt_invanalyticOnNhd_invCITED BYCITES

Cites6

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Cited by1

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