Theorems · Theorem · complex analysis
ContinuousLinearMap.analyticAt
∀ {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)
(x : E), AnalyticAt 𝕜 (⇑f) x- Defined in
- Mathlib.Analysis.Analytic.Linear
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 185 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
- 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
- AnalyticAtstatement · cited by 321
- HasFPowerSeriesAt.analyticAtproof · cited by 11
- ContinuousLinearMap.hasFPowerSeriesAtproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- analyticAt_idproof · cited by 39
- ContinuousLinearMap.analyticOnNhdproof · cited by 5
- analyticOnNhd_circleMapproof · cited by 3
- ContinuousLinearMap.analyticWithinAtproof · cited by 3
- analyticAt_sndproof · cited by 2
- AnalyticOnNhd.eqOn_zero_of_preconnected_of_eventuallyEq_zeroproof · cited by 2
- analyticWithinAt_pi_iffproof · cited by 2
- analyticAt_fstproof · cited by 2
- AnalyticAt.re_ofRealproof · cited by 2
- AnalyticAt.eventually_constant_or_nhds_le_map_nhdsproof · cited by 1
- AnalyticOnNhd.eval_continuousLinearMapproof · cited by 1
- HarmonicAt.analyticAtproof · cited by 0