Theorems · Theorem · several complex variables

AnalyticOnNhd.continuous

∀ {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},
  AnalyticOnNhd 𝕜 f Set.univ → Continuous f

Analytic everywhere implies continuous

Defined in: Mathlib.Analysis.Analytic.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace

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NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
NontriviallyNormedFieldstatement and proof · cited by 8,742
Set.univstatement and proof · cited by 3,945
Continuousstatement · cited by 2,592
AnalyticOnNhdstatement and proof · cited by 206
continuousOn_univproof · cited by 43
AnalyticOnNhd.continuousOnproof · cited by 7

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