Theorems · Theorem · real analysis

uniqueDiffOn_convex_of_isRCLikeNormedField

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] [h𝕜 : IsRCLikeNormedField 𝕜] {E : Type u_2}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedSpace ℝ E] {s : Set E},
  Convex ℝ s → (interior s).Nonempty → UniqueDiffOn 𝕜 s

In a real or complex vector space, a convex set with nonempty interior is a set of unique differentiability.

Defined in

Mathlib.Analysis.RCLike.TangentCone

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldIsRCLikeNormedFieldNormedAddCommGroupNormedSpaceNormedSpace