Theorems · Theorem · complex analysis
analyticWithinAt_of_singleton_mem
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [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},
{x} ∈ nhdsWithin x s → AnalyticWithinAt 𝕜 f s xAnalyticWithinAt is trivial if {x} ∈ 𝓝[s] x
- Defined in
- Mathlib.Analysis.Analytic.Within
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realproof · cited by 25,697
- 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
- add_zeroproof · cited by 2,707
- IsOpenproof · cited by 2,400
- SummationFilter.unconditionalproof · cited by 2,068
- nhdsWithinstatement and proof · cited by 1,912
- ENNReal.ofRealproof · cited by 863
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.