Theorems · Theorem · several complex variables
AnalyticOn.analyticAt
∀ {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} {z : E} {s : Set E},
s ∈ nhds z → AnalyticOn 𝕜 f s → AnalyticAt 𝕜 f z- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- FormalMultilinearSeriesproof · cited by 615
- AnalyticAtstatement · cited by 321
- AnalyticOnstatement and proof · cited by 161
- mem_of_mem_nhdsproof · cited by 126
- HasFPowerSeriesWithinAtproof · cited by 53
- hasFPowerSeriesWithinAt_iff_of_nhdsproof · cited by 1
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