Theorems · Theorem · functional analysis

Seminorm.convex_ball

∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul ℝ 𝕜] [NormSMulClass ℝ 𝕜]
  [inst_4 : Module 𝕜 E] [inst_5 : Module ℝ E] [IsScalarTower ℝ 𝕜 E] (p : Seminorm 𝕜 E) (x : E) (r : ℝ),
  Convex ℝ (p.ball x r)

Seminorm-balls are convex.

Defined in

Mathlib.Analysis.Seminorm

Cited by

4 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupSMulNormSMulClassModuleModuleIsScalarTower