Theorems · Theorem · functional analysis

RCLike.iInter_countable_halfSpaces_eq

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E] {s : Set E}
  [inst_3 : RCLike 𝕜] [inst_4 : Module 𝕜 E] [IsScalarTower ℝ 𝕜 E] [IsTopologicalAddGroup E] [ContinuousSMul 𝕜 E]
  [LocallyConvexSpace ℝ E] [HereditarilyLindelofSpace E],
  Convex ℝ s → IsClosed s → ∃ l c, ⋂ n, {x | RCLike.re ((l n) x) ≤ c n} = s

Defined in

Mathlib.Analysis.LocallyConvex.Separation

Cited by

0 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupModuleRCLikeModuleIsScalarTowerIsTopologicalAddGroupContinuousSMulLocallyConvexSpaceHereditarilyLindelofSpace