Theorems · Theorem · functional analysis
NormedAddGroupHom.mem_ker
∀ {V₁ : Type u_3} {V₂ : Type u_4} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂) (v : V₁), v ∈ f.ker ↔ f v = 0- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddSubgroupstatement and proof · cited by 3,232
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedAddGroupHomstatement and proof · cited by 216
- AddMonoidHom.mem_kerproof · cited by 26
- NormedAddGroupHom.kerstatement · cited by 14
- NormedAddGroupHom.coe_toAddMonoidHomproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.IsQuotient.norm_liftproof · cited by 0
- NormedAddGroupHom.ker_completionproof · cited by 0