Theorems · Theorem · complex analysis
ContinuousLinearMap.analyticOnNhd
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E →L[𝕜] F)
(s : Set E), AnalyticOnNhd 𝕜 (⇑f) s- Defined in
- Mathlib.Analysis.Analytic.Linear
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- AnalyticOnNhdstatement · cited by 206
- ContinuousLinearMap.analyticAtproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.continuousLinearMap_compproof · cited by 6
- IsBoundedLinearMap.contDiffproof · cited by 6
- ContDiffWithinAt.restrict_scalarsproof · cited by 2
- AnalyticOnNhd.im_ofRealproof · cited by 0
- AnalyticOnNhd.re_ofRealproof · cited by 0