Theorems · Theorem · several complex variables
AnalyticOnNhd.continuousOn
∀ {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},
AnalyticOnNhd 𝕜 f s → ContinuousOn f s- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousOnstatement · cited by 1,411
- AnalyticOnNhdstatement and proof · cited by 206
- ContinuousAt.continuousWithinAtproof · cited by 102
- AnalyticAt.continuousAtproof · cited by 35
Cited by7
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
- AnalyticAt.eventually_constant_or_nhds_le_map_nhds_auxproof · cited by 1
- CPolynomialOn.continuousOnproof · cited by 1
- AnalyticOnNhd.continuousproof · cited by 0