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Theorems · Theorem · several complex variables

AnalyticWithinAt.continuousWithinAt_insert

∀ {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} {s : Set E} {x : E},
  AnalyticWithinAt 𝕜 f s x → ContinuousWithinAt f (insert x s) x
Defined in
Mathlib.Analysis.Analytic.Basic
Cited by
3 results in Mathlib
Foundations
Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

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

AnalyticWithinAt.cpow · cited by 2AnalyticWithinAt.cpowHasFPowerSeriesWithinAt.comp · cited by 2HasFPowerSeriesWithinAt.c…AnalyticWithinAt.continuousWithinAt · cited by 2AnalyticWithinAt.continuo…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldFormalMultilinearSeries · cited by 615FormalMultilinearSeriesContinuousWithinAt · cited by 512ContinuousWithinAtAnalyticWithinAt · cited by 96AnalyticWithinAtHasFPowerSeriesWithinAt · cited by 53HasFPowerSeriesWithinAtHasFPowerSeriesWithinAt.continuousWithinAt_insert · cited by 2HasFPowerSeriesWithinAt.c…AnalyticWithinAt.continuousWi…CITED BYCITES

Cites9

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Cited by3

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