Theorems · Theorem · functional analysis
geometric_hahn_banach_point_point
∀ {E : Type u_2} [inst : TopologicalSpace E] [inst_1 : AddCommGroup E] [inst_2 : Module ℝ E] {x y : E}
[IsTopologicalAddGroup E] [ContinuousSMul ℝ E] [LocallyConvexSpace ℝ E] [T1Space E], x ≠ y → ∃ f, f x < f ySee also SeparatingDual.eq_iff_forall_dual_eq.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- 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
- Nat.cast_zeroproof · cited by 1,870
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousSMulstatement and proof · cited by 1,016
- StrongDualstatement and proof · cited by 459
- lt_of_not_geproof · cited by 374
- T1Spacestatement and proof · cited by 275
Cited by1
Results whose statement or proof uses this declaration.
- IsCompact.extremePoints_nonemptyproof · cited by 2