Theorems · Theorem · global analysis
mem_closure_of_nonempty_tangentConeAt
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : SMul 𝕜 E] [inst_2 : TopologicalSpace E] {s : Set E}
{x : E} [ContinuousAdd E], (tangentConeAt 𝕜 s x).Nonempty → x ∈ closure s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- 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
- Set.Nonemptystatement and proof · cited by 2,627
- closurestatement · cited by 1,254
- Filter.NeBotproof · cited by 853
- ContinuousAddstatement and proof · cited by 777
Cited by1
Results whose statement or proof uses this declaration.
- zero_mem_tangentConeAt_iffproof · cited by 1