Theorems · Theorem · global analysis
zero_mem_tangentConeAt
∀ {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}, x ∈ closure s → 0 ∈ tangentConeAt 𝕜 s xThe tangent cone at a non-isolated point contains 0.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- one_smulproof · cited by 1,374
- closurestatement and proof · cited by 1,254
- ContinuousAddstatement and proof · cited by 777
- Filter.Frequentlyproof · cited by 414
- continuous_id'proof · cited by 295
Cited by2
Results whose statement or proof uses this declaration.
- zero_mem_tangentConeAt_iffproof · cited by 1
- zero_mem_tangentConeproof · cited by 0