Theorems · Theorem · functional analysis

Balanced.zero_insert_interior

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {A : Set E}
  [inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E], Balanced 𝕜 A → Balanced 𝕜 (insert 0 (interior A))

The union of {0} with the interior of a balanced set is balanced.

Defined in

Mathlib.Analysis.LocallyConvex.Basic

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul