Theorems · Theorem · global analysis

tangentConeAt_nonempty_of_properSpace

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [ProperSpace E] {s : Set E} {x : E},
  AccPt x (Filter.principal s) → (tangentConeAt 𝕜 s x ∩ {0}ᶜ).Nonempty

In a proper space, the tangent cone at a non-isolated point is nontrivial.

Defined in

Mathlib.Analysis.Calculus.TangentCone.ProperSpace

Cited by

0 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceProperSpace