Theorems · Theorem · global analysis
tangentConeAt_eq_univ
∀ {𝕜 : Type u_1} [inst : NormedDivisionRing 𝕜] {s : Set 𝕜} {x : 𝕜},
AccPt x (Filter.principal s) → tangentConeAt 𝕜 s x = Set.univThe tangent cone at a non-isolated point in dimension 1 is the whole space.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
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
- Set.univstatement · cited by 3,945
- Compl.complproof · cited by 2,925
- nhdsWithinproof · cited by 1,912
- sub_selfproof · cited by 996
- Filter.principalstatement and proof · cited by 740
- Filter.Eventually.monoproof · cited by 646
- Filter.Frequentlyproof · cited by 414
- NormedDivisionRingstatement and proof · cited by 360
- continuous_id'proof · cited by 295
- inf_le_leftproof · cited by 286
- continuous_constproof · cited by 278
Cited by1
Results whose statement or proof uses this declaration.
- uniqueDiffWithinAt_iff_accPtproof · cited by 5