Theorems · Theorem · functional analysis
ContinuousLinearMap.norm_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
- 11 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousLinearMap.idproof · cited by 233
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
- ContinuousLinearMap.norm_smulRight_applyproof · cited by 6
- ContinuousLinearMap.norm_idproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- norm_deriv_eq_norm_fderivproof · cited by 4
- Convex.norm_image_sub_le_of_norm_hasDerivWithin_leproof · cited by 4
- ContinuousLinearMap.nnnorm_toSpanSingletonproof · cited by 1
- Convex.isLittleO_pow_succ_realproof · cited by 1
- HasDerivAt.le_of_lip'proof · cited by 1
- summable_of_summable_hasDerivAt_of_isPreconnectedproof · cited by 1
- hasDerivAt_tsum_of_isPreconnectedproof · cited by 1
- HasDerivAt.le_of_lipschitzproof · cited by 0
- HasDerivAt.le_of_lipschitzOnproof · cited by 0
- norm_derivWithin_eq_norm_fderivWithinproof · cited by 0
- differentiable_tsum'proof · cited by 0