Theorems · Theorem · global analysis
tangentConeAt_subset_zero
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Semiring 𝕜] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousAdd E] {s : Set E} {x : E} [T2Space E],
¬AccPt x (Filter.principal s) → tangentConeAt 𝕜 s x ⊆ 0If x is not an accumulation point of s, then the tangent cone of s at x
is a subset of {0}.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- add_zeroproof · cited by 2,707
- T2Spacestatement and proof · cited by 1,351
- Filter.NeBotproof · cited by 853
Cited by2
Results whose statement or proof uses this declaration.
- UniqueDiffWithinAt.accPtproof · cited by 1
- AccPt.of_mem_tangentConeAt_ne_zeroproof · cited by 0