Theorems · Theorem · general topology
ContinuousMap.norm_coe_le_norm
∀ {α : Type u_1} {E : Type u_3} [inst : TopologicalSpace α] [inst_1 : CompactSpace α]
[inst_2 : SeminormedAddCommGroup E] (f : C(α, E)) (x : α), ‖f x‖ ≤ ‖f‖- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 127 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 · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousMapstatement and proof · cited by 2,491
- CompactSpacestatement and proof · cited by 593
- BoundedContinuousFunction.norm_coe_le_normproof · cited by 25
- BoundedContinuousFunction.mkOfCompactproof · cited by 21
Cited by14
Results whose statement or proof uses this declaration.
- IsGreatest.norm_cfcproof · cited by 6
- IsGreatest.norm_cfcₙproof · cited by 5
- PadicInt.norm_mahlerTermproof · cited by 2
- isBigO_norm_Icc_restrict_atBotproof · cited by 1
- IsUltrametricDist.norm_fwdDiff_iter_apply_leproof · cited by 1
- isBigO_norm_restrict_cocompactproof · cited by 1
- MeasureTheory.integrableOn_iUnion_of_summable_norm_restrictproof · cited by 1
- intervalIntegral.hasSum_intervalIntegral_of_summable_normproof · cited by 1
- Real.integrable_of_summable_norm_Iccproof · cited by 1
- UnitAddTorus.mFourier_normproof · cited by 1
- ContinuousMap.neg_norm_le_applyproof · cited by 0
- ContinuousMap.apply_le_normproof · cited by 0