Theorems · Theorem · global analysis
DifferentiableWithinAt.of_subsingleton
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
[inst_6 : TopologicalSpace F] {f : E → F} {x : E} {s : Set E} [T1Space E],
s.Subsingleton → DifferentiableWithinAt 𝕜 f s x- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- DifferentiableWithinAtstatement · cited by 453
- Set.Subsingletonstatement and proof · cited by 276
- T1Spacestatement and proof · cited by 275
- Set.Subsingleton.finiteproof · cited by 20
- DifferentiableWithinAt.of_finiteproof · cited by 1
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