Theorems · Theorem · functional analysis

geometric_hahn_banach_closed_point

∀ {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E] {s : Set E} {x : E}
  [IsTopologicalAddGroup E] [ContinuousSMul ℝ E] [LocallyConvexSpace ℝ E],
  Convex ℝ s → IsClosed s → x ∉ s → ∃ f u, (∀ a ∈ s, f a < u) ∧ u < f x

Defined in

Mathlib.Analysis.LocallyConvex.Separation

Cited by

2 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommGroupModuleIsTopologicalAddGroupContinuousSMulLocallyConvexSpace