Theorems · Theorem · functional analysis

UniqueDiffWithinAt.smul_iff

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {s : Set E} {x : E} {G : Type u_4} [inst_3 : GroupWithZero G]
  [inst_4 : DistribMulAction G E] [ContinuousConstSMul G E] [SMulCommClass G 𝕜 E] {c : G},
  c ≠ 0 → (UniqueDiffWithinAt 𝕜 (c • s) (c • x) ↔ UniqueDiffWithinAt 𝕜 s x)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceGroupWithZeroDistribMulActionContinuousConstSMulSMulCommClass