Theorems · Theorem · convex and discrete geometry

starConvex_zero_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [AddRightMono 𝕜] [inst_3 : AddCommMonoid E]
  [inst_4 : SMulWithZero 𝕜 E] {s : Set E}, StarConvex 𝕜 0 s ↔ ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃a : 𝕜⦄, 0 ≤ a → a ≤ 1 → a • x ∈ s

Defined in

Mathlib.Analysis.Convex.Star

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

RingPartialOrderAddRightMonoAddCommMonoidSMulWithZero