Theorems · Theorem · functional analysis
SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair
∀ {R : Type u_1} {V : Type u_2} [inst : Field R] [inst_1 : AddCommGroup V] [inst_2 : TopologicalSpace R]
[inst_3 : TopologicalSpace V] [IsTopologicalRing R] [inst_5 : Module R V] [SeparatingDual R V] {x y : V},
x ≠ 0 → y ≠ 0 → ∃ f, f x = 1 ∧ f y ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- 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
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- StrongDualstatement and proof · cited by 459
- IsTopologicalRingstatement and proof · cited by 402
- inv_mul_cancel₀proof · cited by 267
Cited by1
Results whose statement or proof uses this declaration.
- SeparatingDual.exists_continuousLinearEquiv_apply_eqproof · cited by 1