Theorems · Theorem · functional analysis
geometric_hahn_banach_open_open
∀ {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E] {s t : Set E}
[IsTopologicalAddGroup E] [ContinuousSMul ℝ E],
Convex ℝ s → IsOpen s → Convex ℝ t → IsOpen t → Disjoint s t → ∃ f u, (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b- Cited by
- 2 results in Mathlib
- Foundations
- Depth 168 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
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- IsTopologicalAddGroupstatement and proof · cited by 1,394
Cited by2
Results whose statement or proof uses this declaration.
- geometric_hahn_banach_compact_closedproof · cited by 5
- RCLike.geometric_hahn_banach_open_openproof · cited by 0