Theorems · Theorem · functional analysis
ContinuousLinearMap.nnnorm_toSpanSingleton
∀ {𝕜 : Type u_1} {E : Type u_4} [inst : SeminormedAddCommGroup E] [inst_1 : NontriviallyNormedField 𝕜]
[inst_2 : NormedSpace 𝕜 E] (x : E), ‖ContinuousLinearMap.toSpanSingleton 𝕜 x‖₊ = ‖x‖₊- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement · cited by 952
- NNReal.eqproof · cited by 201
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
- ContinuousLinearMap.norm_toSpanSingletonproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Convex.lipschitzOnWith_of_nnnorm_hasDerivWithin_leproof · cited by 3