Theorems · Theorem · global analysis
tangentConeAt_closure
∀ {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] [ContinuousConstSMul 𝕜 E], tangentConeAt 𝕜 (closure s) x = tangentConeAt 𝕜 s x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- IsOpenproof · cited by 2,400
- le_reflproof · cited by 2,061
- closurestatement and proof · cited by 1,254
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- le_imp_le_of_le_of_leproof · cited by 576
- subset_closureproof · cited by 309
Cited by4
Results whose statement or proof uses this declaration.
- uniqueDiffWithinAt_closureproof · cited by 1
- subset_tangentConeAt_prod_leftproof · cited by 1
- mapsTo_tangentConeAt_piproof · cited by 1
- subset_tangentConeAt_prod_rightproof · cited by 1