Theorems · Theorem · functional analysis
NormedAddGroupHom.bounds_bddBelow
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
{f : NormedAddGroupHom V₁ V₂}, BddBelow {c | 0 ≤ c ∧ ∀ (x : V₁), ‖f x‖ ≤ c * ‖x‖}- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 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
- Realstatement and proof · cited by 25,697
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- BddBelowstatement · cited by 401
- NormedAddGroupHomstatement and proof · cited by 216
Cited by3
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.opNorm_le_boundproof · cited by 12
- NormedAddGroupHom.opNorm_zeroproof · cited by 1
- NormedAddGroupHom.opNorm_eq_of_boundsproof · cited by 1