Theorems · Theorem · functional analysis

gaugeSeminorm_ball_one

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} [inst_2 : RCLike 𝕜]
  [inst_3 : Module 𝕜 E] [inst_4 : IsScalarTower ℝ 𝕜 E] {hs₀ : Balanced 𝕜 s} {hs₁ : Convex ℝ s} {hs₂ : Absorbent ℝ s}
  [inst_5 : TopologicalSpace E] [ContinuousSMul ℝ E], IsOpen s → (gaugeSeminorm hs₀ hs₁ hs₂).ball 0 1 = s

Defined in

Mathlib.Analysis.Convex.Gauge

Cited by

0 results in Mathlib

Foundations

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

Assumes

AddCommGroupModuleRCLikeModuleIsScalarTowerTopologicalSpaceContinuousSMul