Theorems · Theorem · functional analysis

RCLike.geometric_hahn_banach_compact_closed

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E]
  {s t : Set E} [inst_3 : RCLike 𝕜] [inst_4 : Module 𝕜 E] [IsScalarTower ℝ 𝕜 E] [IsTopologicalAddGroup E]
  [ContinuousSMul 𝕜 E] [LocallyConvexSpace ℝ E],
  Convex ℝ s →
    IsCompact s →
      Convex ℝ t →
        IsClosed t → Disjoint s t → ∃ f u v, (∀ a ∈ s, RCLike.re (f a) < u) ∧ u < v ∧ ∀ b ∈ t, v < RCLike.re (f b)

Defined in

Mathlib.Analysis.LocallyConvex.Separation

Cited by

3 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupModuleRCLikeModuleIsScalarTowerIsTopologicalAddGroupContinuousSMulLocallyConvexSpace