Theorems · Theorem · global analysis
tangentConeAt_mono_nhds
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : SMul 𝕜 E] [inst_2 : TopologicalSpace E] {s t : Set E}
{x : E} [ContinuousAdd E], nhdsWithin x s ≤ nhdsWithin x t → tangentConeAt 𝕜 s x ⊆ tangentConeAt 𝕜 t x- 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.
Cites23
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
- Top.topproof · cited by 9,680
- Filterstatement · cited by 8,121
- Set.preimageproof · cited by 4,946
- Filter.Tendstoproof · cited by 3,814
- add_zeroproof · cited by 2,707
- nhdsWithinstatement and proof · cited by 1,912
- ContinuousAddstatement and proof · cited by 777
- ClusterPtproof · cited by 138
- tangentConeAtstatement · cited by 54
Cited by2
Results whose statement or proof uses this declaration.
- UniqueDiffWithinAt.mono_nhdsproof · cited by 3
- tangentConeAt_congrproof · cited by 1