Theorems · Theorem · functional analysis
NormedAddGroupHom.bounds_nonempty
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
{f : NormedAddGroupHom V₁ V₂}, ∃ c, c ∈ {c | 0 ≤ c ∧ ∀ (x : V₁), ‖f x‖ ≤ c * ‖x‖}- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Setstatement · cited by 53,352
- 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
- le_of_ltproof · cited by 1,175
- NormedAddGroupHomstatement and proof · cited by 216
- NormedAddGroupHom.boundproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.le_opNormproof · cited by 9
- NormedAddGroupHom.opNorm_nonnegproof · cited by 5