Theorems · Theorem · general topology
ContinuousMap.norm_eq_iSup_norm
∀ {α : Type u_1} {E : Type u_3} [inst : TopologicalSpace α] [inst_1 : CompactSpace α]
[inst_2 : SeminormedAddCommGroup E] (f : C(α, E)), ‖f‖ = ⨆ x, ‖f x‖- Defined in
- Mathlib.Topology.ContinuousMap.Compact
- Cited by
- 4 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.
Cites10
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
- iSupstatement · cited by 2,415
- CompactSpacestatement and proof · cited by 593
- BoundedContinuousFunction.mkOfCompactproof · cited by 21
- BoundedContinuousFunction.norm_eq_iSup_normproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Real.fourierCoeff_tsum_comp_addproof · cited by 1
- ODE.FunSpace.dist_next_nextproof · cited by 1
- fourier_normproof · cited by 1
- ContinuousMap.isometry_realToRCLikeproof · cited by 0