Theorems · Theorem · functional analysis
ContinuousLinearMap.isOpenMap_of_ne_zero
∀ {R : Type u_1} {M : Type u_2} [inst : TopologicalSpace R] [inst_1 : DivisionRing R] [ContinuousSub R]
[inst_3 : AddCommGroup M] [inst_4 : TopologicalSpace M] [ContinuousAdd M] [inst_6 : Module R M] [ContinuousSMul R M]
(f : StrongDual R M), f ≠ 0 → IsOpenMap ⇑fA nonzero continuous linear functional is open.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- DivisionRingstatement and proof · cited by 1,062
- ContinuousSMulstatement and proof · cited by 1,016
- sub_selfproof · cited by 996
- map_addproof · cited by 964
- ContinuousAddstatement and proof · cited by 777
Cited by2
Results whose statement or proof uses this declaration.
- geometric_hahn_banach_openproof · cited by 4
- geometric_hahn_banach_open_openproof · cited by 2