Theorems · Theorem · functional analysis
RCLike.geometric_hahn_banach_open_point
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E] {s : Set E}
{x : E} [inst_3 : RCLike 𝕜] [inst_4 : Module 𝕜 E] [IsScalarTower ℝ 𝕜 E] [IsTopologicalAddGroup E]
[ContinuousSMul 𝕜 E], Convex ℝ s → IsOpen s → x ∉ s → ∃ f, ∀ a ∈ s, RCLike.re (f a) < RCLike.re (f x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- IsScalarTowerstatement and proof · cited by 3,896
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- IsOpenstatement and proof · cited by 2,400
- IsTopologicalAddGroupstatement and proof · cited by 1,394
Cited by1
Results whose statement or proof uses this declaration.
- RCLike.geometric_hahn_banach_point_openproof · cited by 0